Mercurial > hg > mpdl-xml-content

<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC">
  <metadata>
    <dcterms:identifier>ECHO:NSW2F6PF.xml</dcterms:identifier>
    <dcterms:creator identifier="GND:100696198">Weidler, Johann Friedrich</dcterms:creator>
    <dcterms:title xml:lang="la">Jo. Friderici Weidleri Tractatus de machinis hydraulicis toto terrarum orbe maximis Marlyensi et Londinensi et aliis rarioribus similibus in quo mensurae prope ipsas machinas notatae describuntur, et de viribus earum luculenter disseritur</dcterms:title>
    <dcterms:date xsi:type="dcterms:W3CDTF">1726</dcterms:date>
    <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language>
    <dcterms:rights>CC-BY-SA</dcterms:rights>
    <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
    <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
    <parameters>despecs=1.1.2</parameters>
  </metadata>
  <text xml:lang="la" type="free">
<div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/>
<pb file="0002" n="2"/>
<handwritten/>
<handwritten/>
<handwritten/>
<handwritten/>
<pb file="0003" n="3"/>
</div>
<div xml:id="echoid-div2" type="section" level="1" n="2">
<head xml:id="echoid-head1" xml:space="preserve"><emph style="red">IO. FRIDERICI VVEIDLERI</emph></head>
<head xml:id="echoid-head2" xml:space="preserve">TRACTATVS <lb/>DE <lb/>MACHINIS HYDRAVLICIS <lb/>TOTO TERRARVM ORBE MAXIMIS</head>
<head xml:id="echoid-head3" xml:space="preserve"><emph style="red">MARLYENSI</emph> <lb/>ET <lb/><emph style="red">LONDINENSI</emph> <lb/>ET ALIIS RARIORIBVS SIMILIBVS <lb/>IN QVO <lb/><emph style="red">MENSVRAE PROPE IPSAS MACHINAS</emph> <lb/>NOTATAE DESCRIBVNTVR, ET DE VIRIBVS EARVM <lb/>LVCVLENTER DISSERITVR</head>
<head xml:id="echoid-head4" style="it" xml:space="preserve">CVM FIGVRIS AERI INCISIS.</head>
  <figure>
    <image file="0003-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0003-01"/>
  </figure>
</div>
<div xml:id="echoid-div3" type="section" level="1" n="3">
<head xml:id="echoid-head5" xml:space="preserve">EDITIO SECVNDA AVCTIOR</head>
<head xml:id="echoid-head6" style="it" xml:space="preserve">VITEMBERGAE</head>
<head xml:id="echoid-head7" xml:space="preserve"><emph style="red"><emph style="sc">Svmptibvs</emph> CAROLI SIGISMVNDI HENNINGII</emph> <lb/>A. <emph style="sc">c</emph><emph style="sc">Iɔ</emph> <emph style="sc">Iɔ cc xxxiii</emph>.</head>
<pb file="0004" n="4"/>
<pb file="0005" n="5"/>
</div>
<div xml:id="echoid-div4" type="section" level="1" n="4">
<head xml:id="echoid-head8" style="it" xml:space="preserve">SERENISSIMO POTENTISSIMOQVE <lb/>PRINCIPI ET DOMINO</head>
<head xml:id="echoid-head9" xml:space="preserve">DOMINO <lb/>FRIDERICO <lb/>AVGVSTO</head>
<head xml:id="echoid-head10" xml:space="preserve">REGI POLONIARVM</head>
<head xml:id="echoid-head11" xml:space="preserve">MAGNO DVCI LITHAVN. RVSS. PRVSS. <lb/>MASOV. SAMOGIT. KYOV. VOLHIN. PODOL. <lb/>PODLACH. LIVON. SMOLENSK. SEVER. <lb/>SCHERNICOV.</head>
<head xml:id="echoid-head12" xml:space="preserve">DVCI SAXON. IVL. CLIV. MONT. <lb/>ANGAR. ET VVESTPHAL. <lb/>S. R. I. ARCHIMARESCHALLO <lb/>ET PRINCIPI ELECTORI <lb/>LANDGRAV. THVRING. <lb/>MARCH. MISN. ET LVSAT. <lb/>BVRGGRAV. MAGDEB. <lb/>PR. COM. HENNEB. COMIT MARC. <lb/>RAVENSB. ET BARBY <lb/>DOMINO RAVENST. <lb/>ETC. ETC. ETC.</head>
<head xml:id="echoid-head13" style="it" xml:space="preserve">DOMINO MEO LONGE CLEMENTISSIMO</head>
<pb file="0006" n="6"/>
</div>
<div xml:id="echoid-div5" type="section" level="1" n="5">
<head xml:id="echoid-head14" xml:space="preserve">SERENISSIME <lb/>ET <lb/>POTENTISSIME <lb/>REX <emph style="sc">ET</emph> ELECTOR <lb/>DOMINE <lb/>LONGE CLEMENTISSIME</head>
<p>
  <s xml:id="echoid-s1" xml:space="preserve">NOn absque timore <lb/>quodam ad TVAE <lb/>MAIESTATIS <lb/>pedes huncce libel-<lb/>lum uenerabundus depono. </s>
  <s xml:id="echoid-s2" xml:space="preserve">Tam-
<pb file="0007" n="7"/>
etſi enim ea ante aliquot an-<lb/>nos felicitas mihi obtigerit, ut <lb/>mandatu TVO gratioſisſimo <lb/>ſpartam publice interpretandi <lb/>diſciplinas mathematicas adeptus <lb/>fuerim, atque ideo partibus offi-<lb/>cii mei conueniens uideatur, ut <lb/>omnem occaſionem, qua TVAE <lb/>MAIESTATI qualecunque <lb/>ſtudium in munere, quod ſubii, <lb/>exequendo collocatum compro-<lb/>bare posſim, auidisſime arripiam, <lb/>tamen non mediocris animo for-<lb/>mido incutitur, dum conſidero <lb/>non modo auguſtisſimam perſo-<lb/>nae TVAE dignitatem, ſed
<pb file="0008" n="8"/>
etiam peritiam perſpicientiam-<lb/>que TVAM, in omni ſcientia-<lb/>rum genere, et ſpeciatim in eo-<lb/>dem, quod illuſtrare aggreſſus <lb/>ſum, argumento, ſummam, ut <lb/>uix ſpes mihi ſuperſit, iudicio <lb/>TVO limatisſimo has parui <lb/>momenti meditationes ulla ex <lb/>parte eſſe ſatisfacturas. </s>
  <s xml:id="echoid-s3" xml:space="preserve">Enim-<lb/>uero cum ad excelſi animi TVI <lb/>magnitudinem humanitas et in-<lb/>dulgentia prorſus ſingularis ac-<lb/>cedat, qua humiliores quoque, <lb/>pro artibus liberalibus augen-<lb/>dis conatus, ſoles adſpicere, <lb/>quemadmodum ipſemet ego
<pb file="0009" n="9"/>
antehac, oblatis TIBI leuiuſ-<lb/>culis de phoſphoro barometro-<lb/>rum poſitionibus, luculenter ſum <lb/>expertus, et quia praeterea hoc <lb/>in tractatu arduum machinalis <lb/>doctrinae caput, quod Prin-<lb/>cipum cura haud omnino in-<lb/>dignum eſt, uberius traden-<lb/>dum ſumſi, confido fore, ut <lb/>TVA SACRATISSIMA <lb/>MAIESTAS audaciae meae <lb/>benignisſime ignoſcat, et gratia <lb/>ſua optima et maxima ulterius <lb/>me proſequi dignetur. </s>
  <s xml:id="echoid-s4" xml:space="preserve">idemque <lb/>eſt, quod religioſisſime peto, qui <lb/>pro TVA totiusque DOMVS
<pb file="0010" n="10"/>
REGIAE ſalute uota, quoad <lb/>uiuam, ſuſcipere non deſiſtam</s>
</p>
</div>
<div xml:id="echoid-div6" type="section" level="1" n="6">
<head xml:id="echoid-head15" xml:space="preserve">SERENISSIME <lb/><emph style="sc">ET</emph> <lb/>POTENTISSIME <lb/>REX <emph style="sc">ET</emph> ELECTOR <lb/>DOMINE <lb/>LONGE CLEMENTISSIME <lb/>REGIAE TVAE MAIESTATIS</head>
<p style="it">
  <s xml:id="echoid-s5" xml:space="preserve">Vitembergae <lb/>A. </s>
  <s xml:id="echoid-s6" xml:space="preserve">C. </s>
  <s xml:id="echoid-s7" xml:space="preserve">cIɔ Iɔ cc XXIIX. <lb/></s>
  <s xml:id="echoid-s8" xml:space="preserve">XIII. </s>
  <s xml:id="echoid-s9" xml:space="preserve">Kal. </s>
  <s xml:id="echoid-s10" xml:space="preserve">Mart.</s>
  <s xml:id="echoid-s11" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s12" xml:space="preserve">humillimus ſeruus</s>
</p>
<p>
  <s xml:id="echoid-s13" xml:space="preserve"><emph style="sc">Io</emph>. </s>
  <s xml:id="echoid-s14" xml:space="preserve"><emph style="sc">Frider</emph>. </s>
  <s xml:id="echoid-s15" xml:space="preserve"><emph style="sc">Weidler</emph>.</s>
  <s xml:id="echoid-s16" xml:space="preserve"/>
</p>
<pb file="0011" n="11"/>
  <figure>
    <image file="0011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0011-01"/>
  </figure>
</div>
<div xml:id="echoid-div7" type="section" level="1" n="7">
<head xml:id="echoid-head16" xml:space="preserve">PRAEFATIO.</head>
<p style="it">
  <s xml:id="echoid-s17" xml:space="preserve">Inter ea, quae ab artium cultore iter <lb/>ad exteros ſuſcipiente, curioſius at-<lb/>tentiusque conſiderari merentur, <lb/>machinas quoque ingenioſe inuentas, <lb/>feliciterque conſtructas, omnino nu-<lb/>merandas eſſe arbitor. </s>
  <s xml:id="echoid-s18" xml:space="preserve">Fiunt enim <lb/>peregrinationes ſingularium obſer-<lb/>uationum conquirendarum cauſa, <lb/>quales potiſſimum ingens machinamentorum uarietas offert, <lb/>in quibus ſaepe numero locus uſusue nouas ſuggerit uirium <lb/>conſociationes, quae ſine peculiari eiusmodi occaſione pror-<lb/>ſus fuiſſent intermiſſae. </s>
  <s xml:id="echoid-s19" xml:space="preserve">Praeterea machinas non uulgares <lb/>babeo pro totidem grauiſſimis naturae et artis experimentis, <lb/>quae otioſis ſpeculationibus minime praecipiuntur, ſed ſolo <lb/>ex euentu rite diiudicantur. </s>
  <s xml:id="echoid-s20" xml:space="preserve">Siquidem permultum intereſt <lb/>inter fabricam abſolutam, et conceptum animo potentiarum <lb/>nexum, uel earum ſimulacra in cbarta depicta. </s>
  <s xml:id="echoid-s21" xml:space="preserve">Illius effectus <lb/>et una uirtutes et uitia promte patent ſpectatori, qui princi-<lb/>piorum macbinalis ſcientiae non plane imperitus eſt, baec <lb/>autem inuentores ſuos ſaepius fallere et a magna ſpe depellere <lb/>ſolent. </s>
  <s xml:id="echoid-s22" xml:space="preserve">Idemque ideo contingere debet, quia innumera,
<pb o="2" file="0012" n="12" rhead="PRAEFATIO."/>
quae ad corporum motiones, ſpeciatim impetum attritumque <lb/>mutuum eorundem, ſpectant, nos adbuc latent momenta, <lb/>quorum difficultates ſi usquam reuocabuntur ad regulam, ex-<lb/>perientia magiſtra eandem ut patefaciat neceſſum eſt. </s>
  <s xml:id="echoid-s23" xml:space="preserve">Ho-<lb/>rum ego non fui plane immemor, cum nuper Germaniam, <lb/>Belgium, Angliam et Galliam peragrarem, atque in prae-<lb/>ſenti profero in lucem ſpecimen explicationis aliquot machi-<lb/>narum memorabiliorum, quae uel nunquam antea, uel ſal-<lb/>tem obſcurius imperfectiusque, deſeriptae ſunt. </s>
  <s xml:id="echoid-s24" xml:space="preserve">Primo loco <lb/>iure collocanda fuit Marlyenſis, opus uere regium, et tum <lb/>amplitudine ſua tum ſucceſſu admirandum, illius nonnullae <lb/>quidem picturae non inelegantes, icbnographicae et ortbo-<lb/>grapbicae, Pariſiis uenales proſtant, uerum omiſſa eſt ſin-<lb/>gularum partium et finium commemoratio. </s>
  <s xml:id="echoid-s25" xml:space="preserve">unus <emph style="sc">Jonche-<lb/>rivs</emph>, in tractatu, quo nouam muniendi formam uulga-<lb/>uit, nonnibil de bac macbina eſt commentatus, breuiter ta-<lb/>men nimis et conciſe, ut dicendorum non inane ſpicilegium <lb/>reliquiſſe uideatur. </s>
  <s xml:id="echoid-s26" xml:space="preserve">Ob cognationem argumenti ſubiunxi <lb/>percurioſam compoſitionem antliarum, quibus Pariſiis aquae <lb/>ex ſequana flumine attolluntur, et per urbis maximae uicos <lb/>diſtribuuntur. </s>
  <s xml:id="echoid-s27" xml:space="preserve">Tum ſequuntur duae molae alatae bydraulicae, <lb/>baud procul Lutetia Pariſiorum exſtructae, quarum ne qui-<lb/>dem imagines reperire ibidem potui. </s>
  <s xml:id="echoid-s28" xml:space="preserve">interim uſum earum la-<lb/>te patere, ex ſuo loco dicendis manifeſtum fiet. </s>
  <s xml:id="echoid-s29" xml:space="preserve">Denique <lb/>de macbina bydraulica Londinenſi, in qua aer calore uebe-<lb/>menter expanſus, cauſam motus præcipuam conſtituit, tan-<lb/>quam de ſingulari praeſtantiſſimoque ſeculi noſtri inuento, <lb/>copioſius diſſerui, et inprimis recentiſſimam expoſui uariis-<lb/>que obſeruationibus illuſtraui emendationem. </s>
  <s xml:id="echoid-s30" xml:space="preserve">Ita uale, <lb/>Beneuole Lector, et laborem buncce meum utilitati publicae <lb/>iuuandae deſtinatum aequi bonique conſule. </s>
  <s xml:id="echoid-s31" xml:space="preserve">Dab. </s>
  <s xml:id="echoid-s32" xml:space="preserve">Witember-<lb/>gae in Saxonibus. </s>
  <s xml:id="echoid-s33" xml:space="preserve">A. </s>
  <s xml:id="echoid-s34" xml:space="preserve">R. </s>
  <s xml:id="echoid-s35" xml:space="preserve">G. </s>
  <s xml:id="echoid-s36" xml:space="preserve">c I ɔ I ɔ cc XXVII. </s>
  <s xml:id="echoid-s37" xml:space="preserve">V. </s>
  <s xml:id="echoid-s38" xml:space="preserve">Id Decembr.</s>
  <s xml:id="echoid-s39" xml:space="preserve"/>
</p>
<pb o="(3)" file="0013" n="13"/>
</div>
<div xml:id="echoid-div8" type="section" level="1" n="8">
<head xml:id="echoid-head17" xml:space="preserve">TRACTATVS <lb/>DE <lb/>MACHINIS <lb/>QVIBVSDAM HYDRAVLICIS <lb/>RARIORIBVS.</head>
<head xml:id="echoid-head18" xml:space="preserve">CAPVT I. <lb/>DE <lb/>MACHINA MARL YENSI.</head>
<head xml:id="echoid-head19" xml:space="preserve">I.</head>
<p>
  <s xml:id="echoid-s40" xml:space="preserve">Cum ſuperiore ſeculo Ludouicus XIV Gallia-<lb/>rum rex potentiſſimus, in ornanda arce ſua <lb/>Verſalienſi occupatus eſſet, deſideratum <lb/>quoque fuit, ut aquae copioſae, ſonticulis <lb/>efficiendis inſeruiturae, eodem deriuarentur. <lb/></s>
  <s xml:id="echoid-s41" xml:space="preserve">Obtulit igitur Regi eiusque miniſtro primario, I. </s>
  <s xml:id="echoid-s42" xml:space="preserve">B-<lb/>Colberto operam ſuam nobilis Leodienſis de Ville, uſu-<lb/>rus artificiis ciuis ſui Rannequinii, fabri lignarii, quibus <lb/>olim aquas ſubterraneas e fodinis Leodienſibus eduxe-<lb/>rat. </s>
  <s xml:id="echoid-s43" xml:space="preserve">Venerunt ambo in Galliam, Regique propoſue-<lb/>runt, ut ex ſequana, quae bis mille circiter paſſibus Ver-<lb/>ſaliis abeſt, aquae antliis haurirentur, et ſupra collem in-<lb/>teriectum ducerentur. </s>
  <s xml:id="echoid-s44" xml:space="preserve">Erat interim Rannequinius <lb/>fere ἀυαλφάβητ{ος}, ſed manuaria arte excellens, prae-<lb/>tereaque eo laboris genere, quod in ſe ſuſcipiebat, a <lb/>longo tempore exercitatiſſimus. </s>
  <s xml:id="echoid-s45" xml:space="preserve">Verum cum nec lau-<lb/>dare inventa ſua aulae, nec ſecuritatem, ſaltem qua-<lb/>lemcunque, de ſucceſſu conatorum praeſtare poſſet, <lb/>Villanus eiusdem ſocius fabri defectus iſtos ſup-
<pb o="4" file="0014" n="14" rhead="CAPVT I."/>
plebat; </s>
  <s xml:id="echoid-s46" xml:space="preserve">et dum hic in progreſſu operis aliqua for-<lb/>ſan de ſuo adiiceret, evenit, ut pro machinae nouae <lb/>inuentore haberetur. </s>
  <s xml:id="echoid-s47" xml:space="preserve">Ii autem, qui initiis fabricae in-<lb/>terfuerunt, affirmarunt mihi ad unum omnes, Ranne-<lb/>quinium illius verum auctorem et fabricatorem, et Vil-<lb/>lanum commendatorem apud aulam, et ueluti ergo-<lb/>dioctem, extitiffe.</s>
  <s xml:id="echoid-s48" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s49" xml:space="preserve">2. </s>
  <s xml:id="echoid-s50" xml:space="preserve">Primum quidem in radice montis, cui S. </s>
  <s xml:id="echoid-s51" xml:space="preserve">Ger-<lb/>mani oppidum imminet, experimentum antliarum <lb/>aquas ui in altum protrudentium ceperunt, et beneficio <lb/>rotae molae in ripa ſequanae poſitae, aquas ex ſequana in <lb/>ſupremum aggerem, (Terraſſe) qui ibidemante caſtellum <lb/>nouum eſt, omnium qui adſtabant, et ipſius Regis, qui <lb/>coram operis noui effectum uidere dignatus eſt, ad-<lb/>miratione extulerunt. </s>
  <s xml:id="echoid-s52" xml:space="preserve">Deinceps iuſſu Regis ad ſtupen-<lb/>dae molis Marlyenſis conſormationem elaborationem-<lb/>que ſeſe accinxerunt, eamque intra ſeptem annos ab-<lb/>ſoluerunt, Louvoiſio, poſt Colberti obitum, coepta <lb/>ſtrenue urgente et adiuuante. </s>
  <s xml:id="echoid-s53" xml:space="preserve">Dicitur etiam Ranne-<lb/>quinius typum minorem futurae machinae (modelle) <lb/>feciffe et regi monſtraſſe. </s>
  <s xml:id="echoid-s54" xml:space="preserve">Verum, utrum et ubi ille <lb/>nunc ſeruetur, reſciſcere non potui. </s>
  <s xml:id="echoid-s55" xml:space="preserve">Eſt aliquis in <lb/>obſeruatorii regii technophylacio, ſed plane diſſimilis <lb/>operis, nec ad experimentum inſtituendum idoneus.</s>
  <s xml:id="echoid-s56" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s57" xml:space="preserve">3. </s>
  <s xml:id="echoid-s58" xml:space="preserve">Cum autem rotae plures flumini imponendae <lb/>eſſent, et praeterea lapſus aquarum impetuoſior requi-<lb/>reretur, palis muroque agger transuerſus factus, et na-<lb/>uigationi nouo alueo proſpectum eſt, qui iuxta uete-<lb/>rem per quater mille paſſus, a uilla Bezons, usque ad <lb/>S. </s>
  <s xml:id="echoid-s59" xml:space="preserve">Germani pontem, continuatur, Lapſus aquarum <lb/>ſupra hunc aggerem eſt 4. </s>
  <s xml:id="echoid-s60" xml:space="preserve">pedum, flumine alto exi-<lb/>ftente.</s>
  <s xml:id="echoid-s61" xml:space="preserve"/>
</p>
<pb o="5" file="0015" n="15" rhead="CAPVT I. DE MACHINA MARLYENSI."/>
<p>
  <s xml:id="echoid-s62" xml:space="preserve">4. </s>
  <s xml:id="echoid-s63" xml:space="preserve">Totius machinae et ſingularum eius partium <lb/>
<anchor type="note" xlink:label="note-0015-01a" xlink:href="note-0015-01"/>
ueſtigium figura prima ob oculos ponit. </s>
  <s xml:id="echoid-s64" xml:space="preserve">Scilicet <lb/>AA eſt flumen ſequanae.</s>
  <s xml:id="echoid-s65" xml:space="preserve"/>
</p>
<div xml:id="echoid-div8" type="float" level="2" n="1">
<note position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve">TAB. 1. <lb/>Fig. 1.</note>
</div>
<p>
  <s xml:id="echoid-s66" xml:space="preserve">BB ſpatium quadrangulum palis concluſum, cuius <lb/>latus circiter 40. </s>
  <s xml:id="echoid-s67" xml:space="preserve">ſexpedas capit.</s>
  <s xml:id="echoid-s68" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s69" xml:space="preserve">CC. </s>
  <s xml:id="echoid-s70" xml:space="preserve">agger ſupra quem aquae ſuperfluae uoluuntur.</s>
  <s xml:id="echoid-s71" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s72" xml:space="preserve">DD. </s>
  <s xml:id="echoid-s73" xml:space="preserve">clathri, ſiue pali fortiores, pro intercipienda <lb/>glacie, auertendisque nauigiis aut lignis trabalibus, ſi <lb/>qua forte ui fluminis abrepta huc appellerent. </s>
  <s xml:id="echoid-s74" xml:space="preserve">prae-<lb/>terea, prope latus flumini adverſum BB, alii pali pen-<lb/>ſiles ſunt, qui dum demittuntur, etiam minoribus li-<lb/>gnis natantibus, uiam in riuos ſub rotis factos, prae-<lb/>cludunt.</s>
  <s xml:id="echoid-s75" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s76" xml:space="preserve">num. </s>
  <s xml:id="echoid-s77" xml:space="preserve">1. </s>
  <s xml:id="echoid-s78" xml:space="preserve">ueſtigium rotarum 14.</s>
  <s xml:id="echoid-s79" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s80" xml:space="preserve">n. </s>
  <s xml:id="echoid-s81" xml:space="preserve">2. </s>
  <s xml:id="echoid-s82" xml:space="preserve">ſitus quatuor antliarum prementium, quae alte-<lb/>ro axis rotarum manubrio mouentur.</s>
  <s xml:id="echoid-s83" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s84" xml:space="preserve">n. </s>
  <s xml:id="echoid-s85" xml:space="preserve">3. </s>
  <s xml:id="echoid-s86" xml:space="preserve">cruces horizontales, pro ciendis in motum <lb/>catenis, quae uerſus montem ad ſuperiora caſtella pro-<lb/>tenduntur.</s>
  <s xml:id="echoid-s87" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s88" xml:space="preserve">n. </s>
  <s xml:id="echoid-s89" xml:space="preserve">4. </s>
  <s xml:id="echoid-s90" xml:space="preserve">catenae ipſae, quarum modo mentionem feci.</s>
  <s xml:id="echoid-s91" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s92" xml:space="preserve">n. </s>
  <s xml:id="echoid-s93" xml:space="preserve">5. </s>
  <s xml:id="echoid-s94" xml:space="preserve">ripa fluminis et uia ſub catenis, qua Pariſiis <lb/>S. </s>
  <s xml:id="echoid-s95" xml:space="preserve">Germanum itur.</s>
  <s xml:id="echoid-s96" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s97" xml:space="preserve">F, F, aedes impoſitae receptaculis aquarum, quae <lb/>per antlias, cum rotis connexas, hauſtae et in ferreis <lb/>fiſtulis eodem deriuatae ſunt. </s>
  <s xml:id="echoid-s98" xml:space="preserve">Vocantur gallis Puiſards <lb/>d’ amy cote, ſiue putei medii, quia inter machinam et <lb/>ſuperiora aquarum receptacula ſunt, latine caſtella media <lb/>nominabo. </s>
  <s xml:id="echoid-s99" xml:space="preserve">Diſtant a flumine 100 circiter ſexpedis. </s>
  <s xml:id="echoid-s100" xml:space="preserve">eo <lb/>a ſequana progrediendo paſſus 332, qui 664. </s>
  <s xml:id="echoid-s101" xml:space="preserve">pedibus <lb/>Pariſinis fere aequipollent, numeraui. </s>
  <s xml:id="echoid-s102" xml:space="preserve">Horum caſtel-<lb/>lorum alterum, ſiniſtrum aſcendentibus, nuncupatur <lb/>paruum, (Gall. </s>
  <s xml:id="echoid-s103" xml:space="preserve">puiſard de petits chevalets) quia anguſtius <lb/>eſt, ſiquidem tantum ſeptem catenarum ordines eo
<pb o="6" file="0016" n="16" rhead="CAPVT I."/>
perueniunt. </s>
  <s xml:id="echoid-s104" xml:space="preserve">ab eodem deorſum abeſt 25. </s>
  <s xml:id="echoid-s105" xml:space="preserve">ſexpedis, pu-<lb/>teus ſcaturiginum, G, quo nimirum aquae ex ſcaturigini-<lb/>bus, quae in uicinis montibus oriuntur, defluunt, et <lb/>hinc antliis in receptaculum E reducuntur.</s>
  <s xml:id="echoid-s106" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s107" xml:space="preserve">F ſpeciatim uocatur caſtellum maius. </s>
  <s xml:id="echoid-s108" xml:space="preserve">aedes enim <lb/>ſunt ampliores, et eo tredecim catenarum paria con-<lb/>tinuantur. </s>
  <s xml:id="echoid-s109" xml:space="preserve">iuxta idem eſt</s>
</p>
<p>
  <s xml:id="echoid-s110" xml:space="preserve">H ſtagnum to ſexp. </s>
  <s xml:id="echoid-s111" xml:space="preserve">latum, 90 ſexp longum, in quod <lb/>exonerantur aquae a fiſtulis, a flumine uenientibus. </s>
  <s xml:id="echoid-s112" xml:space="preserve">uti <lb/>infra copioſius explicabitur. </s>
  <s xml:id="echoid-s113" xml:space="preserve">nolui tamen integrum hu-<lb/>ius ſtagni ueſtigium delineare, quia figurae ſeptimae <lb/>ſpatium reliquum deſtinaueram.</s>
  <s xml:id="echoid-s114" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s115" xml:space="preserve">K ſunt fiſtulae ferreae, quae aquas ex caſtello ſiniſtro <lb/>in ſupremum receptaculum L aduehunt. </s>
  <s xml:id="echoid-s116" xml:space="preserve">et prope hoc <lb/>iacet M caſtellum ſupremum, remotum a mediis 218 ſexpe-<lb/>dis, ſiue 770 paſſibus meis. </s>
  <s xml:id="echoid-s117" xml:space="preserve">eo ex caſtello medio dextro <lb/>porriguntur tredecim catenarum paria, quae antliis ſu-<lb/>premis motu inſtruendis ſeruiunt. </s>
  <s xml:id="echoid-s118" xml:space="preserve">Ceterum neque <lb/>harum aedium iuſtam a mediis diſtantiam potui indi-<lb/>care, quia chartae longitudo minime ſufficiebat. </s>
  <s xml:id="echoid-s119" xml:space="preserve">qua-<lb/>propter hic defectus menſuris nunc indicatis ſuppleri <lb/>et emendari debet.</s>
  <s xml:id="echoid-s120" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s121" xml:space="preserve">O eſt puteus, in quo aquae defluentes ex fiſtulis ant-<lb/>liisque, quae periturae erant, colliguntur, et antliis re-<lb/>ducuntur.</s>
  <s xml:id="echoid-s122" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s123" xml:space="preserve">N. </s>
  <s xml:id="echoid-s124" xml:space="preserve">ſunt ordines aliquot ſiſtularum ferrearum, quae <lb/>tandem aquas in turrim et aquaeductum euehunt, qua-<lb/>rum amplior deſcriptio poſtea ſequetur.</s>
  <s xml:id="echoid-s125" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s126" xml:space="preserve">5. </s>
  <s xml:id="echoid-s127" xml:space="preserve">Cuiuis rotae alueus ſuus praeparatus, et palis at-<lb/>que aſſeribus clauſus eſt, rota uix duobus pedibus am-<lb/>plior. </s>
  <s xml:id="echoid-s128" xml:space="preserve">Riui aquarum in hos alueos admittuntur, leua-<lb/>tis oſtiis, auxilio nempe duarum cochlearum, quae <lb/>uectibus torquentur, et motus laudatorum oſtiorum
<pb o="7" file="0017" n="17" rhead="DE MACHINA MARLYENSI."/>
intra lineam 4 uel 5 pedum continetur. </s>
  <s xml:id="echoid-s129" xml:space="preserve">in Fig. </s>
  <s xml:id="echoid-s130" xml:space="preserve">7. </s>
  <s xml:id="echoid-s131" xml:space="preserve">num. </s>
  <s xml:id="echoid-s132" xml:space="preserve">8. <lb/></s>
  <s xml:id="echoid-s133" xml:space="preserve">Tab. </s>
  <s xml:id="echoid-s134" xml:space="preserve">1. </s>
  <s xml:id="echoid-s135" xml:space="preserve">perſpicue orthographia cochleae oſtio iunctae <lb/>cernitur.</s>
  <s xml:id="echoid-s136" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s137" xml:space="preserve">6. </s>
  <s xml:id="echoid-s138" xml:space="preserve">Rotae, uti figura prima indicat, alternatim poſi-<lb/>tae ſunt, quemadmodum alueorum ducendorum ratio <lb/>poſtulabat, et quoniam omnes una linea, ob appara-<lb/>tum membrorum, quae manubriis adhaerent, contine-<lb/>ri haud poterant, duo earum ordines conſtituti ſunt. <lb/></s>
  <s xml:id="echoid-s139" xml:space="preserve">Primum aduerſo flumini opponuntur rotae ſeptem, ſe-<lb/>quuntur ſecunda ſerie ſex, et tandem una poſt duos or-<lb/>dines ſuſpenſa eſt. </s>
  <s xml:id="echoid-s140" xml:space="preserve">Diameter rotarum ſingularum, ex-<lb/>cepta ultima, ceteris 4 pedibus altiore, eſt 36 pedum, <lb/>axis ligneus habet diametrum 2 {1/2} p. </s>
  <s xml:id="echoid-s141" xml:space="preserve">radii numero 12 <lb/>(ſiquidem ſemper duo paralleli peripheriam portant) <lb/>digitos 8 lati 5 dig. </s>
  <s xml:id="echoid-s142" xml:space="preserve">ſpisſi, ſuſtinent arcus peripheriae du-<lb/>plices, eiusdem fere latitudinis et ſpiſſitudinis. </s>
  <s xml:id="echoid-s143" xml:space="preserve">ſupra <lb/>hanc peripheriam ligneis retinaculis, et baculis quoque <lb/>transuerſis, firmantur aſſeres unum pedem lati, 5 uel 6 <lb/>pedes longi, qui ueluti alas uel gradus horum orbium <lb/>conſtituunt. </s>
  <s xml:id="echoid-s144" xml:space="preserve">Numerus autem eorum non ſemper, nec <lb/>in omnibus ac ſingulis rotis idem eſt. </s>
  <s xml:id="echoid-s145" xml:space="preserve">Poſſunt nimi-<lb/>rum 32 alae orbibus incumbere, quin etiam in interna <lb/>peripheria pro aliis collocandis retinacula aptata ſunt. </s>
  <s xml:id="echoid-s146" xml:space="preserve"><lb/>Verum qualis numerus rotae loco, copiaeue aquarum <lb/>conueniat, optime ſciunt, qui quotidie motum machi-<lb/>nae diligentius obſeruant. </s>
  <s xml:id="echoid-s147" xml:space="preserve">Nam quae in medio flu-<lb/>mine pendent rotae, ob celeritatem ac impetum aqua-<lb/>rum irruentium, non ſemper magno alarum numero <lb/>opus habent, inprimis quando flumen altum eſt; </s>
  <s xml:id="echoid-s148" xml:space="preserve">quae <lb/>uero feriuntur a riuis reliquis remotioribus, a medio <lb/>pluribus et latioribus et quandoque internis alis in-<lb/>ſtrui debent. </s>
  <s xml:id="echoid-s149" xml:space="preserve">Ceterum de manubriis officioque rota-<lb/>rum poſtea a getur.</s>
  <s xml:id="echoid-s150" xml:space="preserve"/>
</p>
<pb o="8" file="0018" n="18" rhead="CAPVT I."/>
<p>
  <s xml:id="echoid-s151" xml:space="preserve">7. </s>
  <s xml:id="echoid-s152" xml:space="preserve">Antliae machinae Marlyenſis triplicis ſunt gene-<lb/>
<anchor type="note" xlink:label="note-0018-01a" xlink:href="note-0018-01"/>
ris. </s>
  <s xml:id="echoid-s153" xml:space="preserve">Prima eſt aſpirans, (gallis pompe aſpirante) ubi <lb/>embolus geſtat ualuulam ſuam C, Fig 2. </s>
  <s xml:id="echoid-s154" xml:space="preserve">Nimirum <lb/>fiſtula D altero extremo aquis immerſa eſt, altero ual-<lb/>uulam B, quae tantum ſurſum aperitur, habet; </s>
  <s xml:id="echoid-s155" xml:space="preserve">in tubo <lb/>uero, qui huic fiſtulae imponitur, embolus ligneus C <lb/>ſimilem habet ualuulam, ſurſum aperiendam. </s>
  <s xml:id="echoid-s156" xml:space="preserve">Dum <lb/>enim adducitur embolus, clauditur eius oſtium, ab <lb/>atmoſphaerae incumbentis pondere, ſub embolo au-<lb/>tem uacuum ab aere craſſo ſpatium efficitur, quod ubi <lb/>contingit, aer tantum premit aquas, quibus extremum <lb/>D immerſum eſt, ut hae, aperta ualuula B, in cylindrum <lb/>ſuperiorem aſcendant, ex quo tandem altius tolluntur, <lb/>depreſſo eodem embolo, et aperta eiusdem ualuula, <lb/>ultra quam cum aquae aſſurrexerunt, ualuula, preſſio-<lb/>ne ceſſante, recluditur. </s>
  <s xml:id="echoid-s157" xml:space="preserve">Valuulae in antliis et fiſtulis <lb/>reliquis Marlyenſibus coriaceae adhibentur. </s>
  <s xml:id="echoid-s158" xml:space="preserve">corium <lb/>nempe tres lineas ſpiſſum duplex iungitur, in medio <lb/>orbis E Fig. </s>
  <s xml:id="echoid-s159" xml:space="preserve">2. </s>
  <s xml:id="echoid-s160" xml:space="preserve">maior minorue, pro ratione oſtii, cui <lb/>reſpondet, exſecatur, relicta circiter quarta peripheriae <lb/>parte integra, quae verticulum efficit, praeterea corio <lb/>duplici ferrea lamina imponitur, et cum eodem colli-<lb/>gatur, quae curuationem corii impedit. </s>
  <s xml:id="echoid-s161" xml:space="preserve">inſeruntur <lb/>haec coria fiſtulis, eo loco, ubi earum extremi orbes <lb/>cochleis nectuntur, et praeter ualuularum officium, <lb/>tum etiam aliud praeſtant, quando applicata orbibus <lb/>fiſtularum rudibus et impolitis, caua eorum replent, et <lb/>omnem aeri acceſſum praecludunt,</s>
</p>
<div xml:id="echoid-div9" type="float" level="2" n="2">
<note position="left" xlink:label="note-0018-01" xlink:href="note-0018-01a" xml:space="preserve">Fig. 2.</note>
</div>
<p>
  <s xml:id="echoid-s162" xml:space="preserve">8. </s>
  <s xml:id="echoid-s163" xml:space="preserve">Antlia ſecundi generis eſt aſpirans et premens, (gall. <lb/></s>
  <s xml:id="echoid-s164" xml:space="preserve">pompe aſpirante et foulante) cuius embolus ligneus ſoli-<lb/>dus, et ſpiſſo corio, clauis cupreis circa medium affi-<lb/>xo, ueſtitus, ita ut altera pars corii ſurſum, altera de-<lb/>orſum uertatur, lignum vero undique ambiat, efficiat-
<pb o="9" file="0019" n="19" rhead="DE MACHINA MARLYENSI."/>
que, utidem perfecte cauo cylindri reſpondeat, omnem-<lb/>que aerem auertat, ſiue aſcendat, ſiue deſcendat. </s>
  <s xml:id="echoid-s165" xml:space="preserve">v. <lb/></s>
  <s xml:id="echoid-s166" xml:space="preserve">Fig. </s>
  <s xml:id="echoid-s167" xml:space="preserve">3. </s>
  <s xml:id="echoid-s168" xml:space="preserve">Alteri autem huius cylindri caui extremo duae <lb/>fiſtulae A et C adhaerent. </s>
  <s xml:id="echoid-s169" xml:space="preserve">prior earum A in aquis ſuo <lb/>extremo recuruo pendet, et plumbea, qua partem pen-<lb/>dulam, fieri poteſt, ſed pars, cui ualuula incumbit, cu-<lb/>prea eſſe debet, quo ſuſtinere queat preſſionem fluidi, <lb/>quando idem embolus protrudit. </s>
  <s xml:id="echoid-s170" xml:space="preserve">ſimiliter fiſtula al-<lb/>tera C, quae ductus aquarum (la conduite gall.) </s>
  <s xml:id="echoid-s171" xml:space="preserve">nomina-<lb/>tur, altero extremo, cui ualuula inſeritur, cuprea requi-<lb/>ritur, ob eandem rationem, reliqua ferrea ſit oportet, <lb/>quia per hanc quoque uis emboli prementis continua-<lb/>tur. </s>
  <s xml:id="echoid-s172" xml:space="preserve">Quod attinet ipſam antliae agitationem et effe-<lb/>ctum, figura tertia iterum conſulenda eſt. </s>
  <s xml:id="echoid-s173" xml:space="preserve">nimirum ad-<lb/>ducto ſurſum embolo B, in locum eius, per canalem <lb/>A et apertum eius oſtium, aſcendunt aquae, uiolentae <lb/>aereae molis preſſioni cedentes; </s>
  <s xml:id="echoid-s174" xml:space="preserve">reducto ligno emboli, <lb/>clauditur ualuula fiſtulae A, et altera prope C in aquae-<lb/>ductum hiat, hunc ergo aquae ingrediuntur, ſed ual-<lb/>uula, ceſſante emboli protruſione, relabitur, et ita re-<lb/>petitis pulſibus, ſemper altius aqua in fiſtula C euehi-<lb/>tur. </s>
  <s xml:id="echoid-s175" xml:space="preserve">De nexu cylindrorum fiſtularumque deinceps <lb/>nonnulla ſuperaddam. </s>
  <s xml:id="echoid-s176" xml:space="preserve">Illud uero omitti non debet, <lb/>quod ſecundi generis antlia, affluxu perpetuo aqua-<lb/>rum in cylindrum, in quo ligneus embolus agitur, opus <lb/>habeat, ſiquidem omnis illius uis conſiſtit, in iuſta <lb/>eius magnitudine, quoad cauum cyiindri, haec ſine <lb/>coriorum laxitate non obtinetur, et laxitas tandem <lb/>aquis conſeruatur. </s>
  <s xml:id="echoid-s177" xml:space="preserve">nam alias coria rigeſcerent, et exſic-<lb/>cata attritu continuo conſumerentur, et breui cylindrum <lb/>antliae non eſſent repletura. </s>
  <s xml:id="echoid-s178" xml:space="preserve">Vt itaque humida per-<lb/>petuo ſint coria, iuxta aſpirantes et prementes antlias <lb/>plures, una aſpirans conſtituenda eſt, quae aquas attol-
<pb o="10" file="0020" n="20" rhead="CAPVT I."/>
lat, embolos reliquarum irrigaturas. </s>
  <s xml:id="echoid-s179" xml:space="preserve">Praeterea ligna <lb/>embolorum alnea ſient, annulis ferreis circummunita, <lb/>quae diu, antequam in antlias inſeruntur, aquis immer-<lb/>ſa iacuerunt. </s>
  <s xml:id="echoid-s180" xml:space="preserve">nam ſic eadem durabiliora et ſolidiora <lb/>euadere, experientia comprobauit.</s>
  <s xml:id="echoid-s181" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s182" xml:space="preserve">9. </s>
  <s xml:id="echoid-s183" xml:space="preserve">Tertii generis antlia eſt inuerſa, (gall. </s>
  <s xml:id="echoid-s184" xml:space="preserve">pompe renuer-<lb/>ſée) fig. </s>
  <s xml:id="echoid-s185" xml:space="preserve">4. </s>
  <s xml:id="echoid-s186" xml:space="preserve">cylindri nempe patens oſtium B deorſum, al-<lb/>terum A, quod ualuula clauditur, ſurſum uertitur, to-<lb/>tusque cylindrus ita inter ligna fortiora ſuſpenditur, ut <lb/>prementis emboli robur ſuſtinere ualeat. </s>
  <s xml:id="echoid-s187" xml:space="preserve">hic cylindrus <lb/>AB plerumque tantum aliquot pedes altus eſt, v. </s>
  <s xml:id="echoid-s188" xml:space="preserve">g. </s>
  <s xml:id="echoid-s189" xml:space="preserve">4, <lb/>6, p. </s>
  <s xml:id="echoid-s190" xml:space="preserve">quia tantum deſtinatur columnis aquarum ab <lb/>embolo ſurſum in aliam fiſtulam trudendis. </s>
  <s xml:id="echoid-s191" xml:space="preserve">Embo-<lb/>lus huius antliae E, itidem ligneus inuerſus, gaudet tri-<lb/>bus quatuorue foraminibus, quae teguntur forti corio <lb/>duplici, ferrum perpendiculare, cui affixus eſt embo-<lb/>lus, incumbit lateri parallelogrammi rectanguli C D, <lb/>quod beneficio anſae ſiue longurii G H, attolli demit-<lb/>tique poteſt. </s>
  <s xml:id="echoid-s192" xml:space="preserve">Scilicet, extremum cylindri B intra <lb/>aquas eſt, et cum demittitur embolus E, coria eiusdem, <lb/>quae ſtringunt cylindri parietes, eleuantur ſupra em-<lb/>bolum, et uiam aquis ab aere grauatis, per foramina <lb/>emboli liberam relinquunt, quae ideo omne ſpatium, <lb/>quod ſupra embolum in cylindro ſupereſt, replent. <lb/></s>
  <s xml:id="echoid-s193" xml:space="preserve">Eleuato deinceps iterum embolo, coria in foramina <lb/>emboli relabuntur, et eadem obturant, atque hinc <lb/>aquae aperiunt ualuulam canalis F, et in eum ſeſe reci-<lb/>piunt, quo facto, deſinente emboli impulſu, ualuula <lb/>A clauditur.</s>
  <s xml:id="echoid-s194" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s195" xml:space="preserve">10. </s>
  <s xml:id="echoid-s196" xml:space="preserve">Quando in hac antlia inuerſa embolus non am-<lb/>plius replet cylindrum, uacillant latera rectanguli, cum <lb/>idem aſcendit, et tum tollitur a longurio ſuo rectangu-<lb/>lum, exemto clauo, et unco, qui ex laqueo circa troch-
<pb o="11" file="0021" n="21" rhead="DE MACHINA MARLYENSI."/>
leam ducto pendet, idem apprehenditur, lenteque ſitu <lb/>perpendiculari demittitur, donec exeat ex cylindro <lb/>embolus, tum idem una cum rectangulo, beneficio axis <lb/>cum peritrochio, attollitur, et emboli uitia corrigun-<lb/>tur, eodemque organo etiam embolus reſtituitur.</s>
  <s xml:id="echoid-s197" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s198" xml:space="preserve">11. </s>
  <s xml:id="echoid-s199" xml:space="preserve">Quod attinet ad canales uel fiſtulas machinae lau-<lb/>datae, cylindri quidem antliarum omnes ferrei ſunt, <lb/>diuerſae amplitudinis et longitudinis pro ratione fini-<lb/>um diuerſa. </s>
  <s xml:id="echoid-s200" xml:space="preserve">aſpirantes ſunt plumbeae, uti ante dixi, <lb/>usque ad utres, in quibus ualuulae iacent, hos enim <lb/>cupreos facere oportuit, et tales etiam ſunt curuatae <lb/>portiones ductuum ſiue canaliculorum, per quos aquae <lb/>protruduntur. </s>
  <s xml:id="echoid-s201" xml:space="preserve">reliquae fiſtulae ferro fuſo conſtant, ple-<lb/>raeque 3 p. </s>
  <s xml:id="echoid-s202" xml:space="preserve">longae, inſtructae perſoratis orbibus planis, <lb/>tetragonis uel polygonis, his enim cochleae intrudun-<lb/>tur, ad tubos connectendos. </s>
  <s xml:id="echoid-s203" xml:space="preserve">nonnunquam ubi magna <lb/>curuatio requiritur, cuprei intermiſcentur. </s>
  <s xml:id="echoid-s204" xml:space="preserve">Inter or-<lb/>bes cochleis conſtrictos coria ad arcendum aerem po-<lb/>nuntur, in quibusdam praeterea plumbum rimis infu-<lb/>ſum notaui.</s>
  <s xml:id="echoid-s205" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s206" xml:space="preserve">12. </s>
  <s xml:id="echoid-s207" xml:space="preserve">Poſt haec coniunctio plurium fiſtularum attendi <lb/>meretur. </s>
  <s xml:id="echoid-s208" xml:space="preserve">Cum enim expulſa embolis aqua, una quo-<lb/>que multum aeris in ductus aquarum prouoluatur, qui <lb/>quando in fiſtulis haeret, non parum aquarum progreſ-<lb/>ſum remoratur, hinc artifices, qui opus, de quo expono, <lb/>compoſuerunt, aquas ex duabus pluribusue fiſtulis in <lb/>unam ampliorem ducere allaborarunt, quod effece-<lb/>runt, coniuncta communi fiſtula cum reliquis, benefi-<lb/>cio curuatorum canalium cupreorum, quo facto, fur-<lb/>cae figura producitur, fig. </s>
  <s xml:id="echoid-s209" xml:space="preserve">5. </s>
  <s xml:id="echoid-s210" xml:space="preserve">et ne aqua recidens impe-<lb/>diret alterius ingreſſum, ualuulis, quae in extremis ca-<lb/>nalium connectendorum inſeruntur, proſpectum eſt. <lb/></s>
  <s xml:id="echoid-s211" xml:space="preserve">praeter tales ualuulas nulla eſt, in aquarum ductibus,
<pb o="12" file="0022" n="22" rhead="CAPVT I."/>
ſiue fiſtulis, quae ducunt aquas per embolos protruſas. <lb/></s>
  <s xml:id="echoid-s212" xml:space="preserve">Valuularum conſtructio ex ſuperioribus intelligitur.</s>
  <s xml:id="echoid-s213" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s214" xml:space="preserve">13. </s>
  <s xml:id="echoid-s215" xml:space="preserve">Venio ad explicandum rotarum officium, quod <lb/>duplex eſt. </s>
  <s xml:id="echoid-s216" xml:space="preserve">Primum agitant antlias prementes, et aquas <lb/>per fiſtulas in ſuperiora duo caſtella media propellunt. <lb/></s>
  <s xml:id="echoid-s217" xml:space="preserve">deinde mouent antlias caſtellorum trium, quorum ſu-<lb/>pra §. </s>
  <s xml:id="echoid-s218" xml:space="preserve">4. </s>
  <s xml:id="echoid-s219" xml:space="preserve">ſitum indicaui, idque ope catenarum eousque <lb/>continuatarum. </s>
  <s xml:id="echoid-s220" xml:space="preserve">Vtrumque officium rotae exequun-<lb/>tur manubriis uerſatilibus. </s>
  <s xml:id="echoid-s221" xml:space="preserve">Nimirum axis rotarum <lb/>quernus longus eſt 15 p. </s>
  <s xml:id="echoid-s222" xml:space="preserve">ſpiſſus 2 {1/2} p. </s>
  <s xml:id="echoid-s223" xml:space="preserve">ex hoc axe ligneo <lb/>prominent utrimque manubria fortiſſima ferrea, fig. </s>
  <s xml:id="echoid-s224" xml:space="preserve">X. </s>
  <s xml:id="echoid-s225" xml:space="preserve"><lb/>Tab. </s>
  <s xml:id="echoid-s226" xml:space="preserve">I. </s>
  <s xml:id="echoid-s227" xml:space="preserve">quorum portio AB prope axem cylindrica I p. </s>
  <s xml:id="echoid-s228" xml:space="preserve"><lb/>longa 6. </s>
  <s xml:id="echoid-s229" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s230" xml:space="preserve">ſpiſſa, altera BC priſmatica 3 p. </s>
  <s xml:id="echoid-s231" xml:space="preserve">longa <lb/>8 dig. </s>
  <s xml:id="echoid-s232" xml:space="preserve">ſpiſſa eſt, extrema pars CD cylindrica 1 p. </s>
  <s xml:id="echoid-s233" xml:space="preserve">longa, <lb/>4. </s>
  <s xml:id="echoid-s234" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s235" xml:space="preserve">craſſa eſt. </s>
  <s xml:id="echoid-s236" xml:space="preserve">pondus plerumque 1500 uel 2000 li-<lb/>brar. </s>
  <s xml:id="echoid-s237" xml:space="preserve">ſingula habent.</s>
  <s xml:id="echoid-s238" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s239" xml:space="preserve">14. </s>
  <s xml:id="echoid-s240" xml:space="preserve">Rotae igitur in prima ſerie, ſingulae altero ma-<lb/>nubrio, quod montem ſpectat, antlias mouent, altero <lb/>par catenarum ducunt; </s>
  <s xml:id="echoid-s241" xml:space="preserve">prima tamen ob ſitum com-<lb/>modum, utroque axis extremo catenas trahit. </s>
  <s xml:id="echoid-s242" xml:space="preserve">Rotae <lb/>ſex ſecundi ordinis catenis utrimque mouendis deſti-<lb/>natae ſunt. </s>
  <s xml:id="echoid-s243" xml:space="preserve">decimae quartae utrimque antliae adhae-<lb/>rent. </s>
  <s xml:id="echoid-s244" xml:space="preserve">Cuilibet autem uectis librantis extremo qua-<lb/>tuor emboli antliarum prementium reſpondent, qua-<lb/>propter in ipſo flumine continuo mouentur ſexaginta <lb/>quatuor antliae prementes, et octo aſpirantes. </s>
  <s xml:id="echoid-s245" xml:space="preserve">Simi-<lb/>liter inde euidens eſt numerus catenarum duplicium. <lb/></s>
  <s xml:id="echoid-s246" xml:space="preserve">Nam in primo ordine rotarum, ſex manubria totidem <lb/>catenas, una catenas duas, et in ſecundo ordine ſex ro-<lb/>tae utrimque catenas habent. </s>
  <s xml:id="echoid-s247" xml:space="preserve">Inde conficitur ſumma <lb/>uiginti parium catenarum. </s>
  <s xml:id="echoid-s248" xml:space="preserve">ſeptem ex his in caſtello <lb/>medio ſiniſtro finiuntur, tredecim ad dextrum caſtel-<lb/>lum aſcendunt; </s>
  <s xml:id="echoid-s249" xml:space="preserve">et tandem in ſupremum caſtellum aſ-<lb/>ſurgunt.</s>
  <s xml:id="echoid-s250" xml:space="preserve"/>
</p>
<pb o="13" file="0023" n="23" rhead="DE MACHINA MARLYENSI."/>
<p>
  <s xml:id="echoid-s251" xml:space="preserve">15. </s>
  <s xml:id="echoid-s252" xml:space="preserve">Antlias flumini impoſitas rotae ſequenti modo in <lb/>
<anchor type="note" xlink:label="note-0023-01a" xlink:href="note-0023-01"/>
motum cient. </s>
  <s xml:id="echoid-s253" xml:space="preserve">Ex uerſatili manubrio pendet tignum <lb/>num. </s>
  <s xml:id="echoid-s254" xml:space="preserve">6, circiter longum 9 p. </s>
  <s xml:id="echoid-s255" xml:space="preserve">craſſum anteriore parte <lb/>8 dig. </s>
  <s xml:id="echoid-s256" xml:space="preserve">hoc altero extremo copulatur cum crucis ligneae <lb/>uerticali ſitu ſuſpenſae num. </s>
  <s xml:id="echoid-s257" xml:space="preserve">4. </s>
  <s xml:id="echoid-s258" xml:space="preserve">perpendiculo, (crucis <lb/>trabs ſuperior transuerſa eſt, longa 12 p. </s>
  <s xml:id="echoid-s259" xml:space="preserve">cathetus 6 p.) <lb/></s>
  <s xml:id="echoid-s260" xml:space="preserve">quod cum tigno transuerſo uinculis ligneis, et inſuper <lb/>duobus ferreis copulatur. </s>
  <s xml:id="echoid-s261" xml:space="preserve">altero autem extremo tigni <lb/>transuerſi C. </s>
  <s xml:id="echoid-s262" xml:space="preserve">trahitur lignum pendulum E C, diuerſae <lb/>longitudinis, pro altitudine libramentorum diuerſa. </s>
  <s xml:id="echoid-s263" xml:space="preserve"><lb/>quod annexum eſt uecti, ſiue librili F G (long. </s>
  <s xml:id="echoid-s264" xml:space="preserve">13 p. </s>
  <s xml:id="echoid-s265" xml:space="preserve">ſpiſſ. </s>
  <s xml:id="echoid-s266" xml:space="preserve"><lb/>18 dig. </s>
  <s xml:id="echoid-s267" xml:space="preserve">et praeterea aliud tignum annulis ferreis colli-<lb/>gatum incumbit, ſimilis fere ſpiſſitudinis, ut incuruatio <lb/>et fractio, quae quandoque ſingularibus tignis accidit, <lb/>caueatur.) </s>
  <s xml:id="echoid-s268" xml:space="preserve">quod ſuper axe ferreo in medio firmato, uol-<lb/>uitur, et utroque extremo duo tigna priſmatica 12 p. </s>
  <s xml:id="echoid-s269" xml:space="preserve"><lb/>longa geſtat, ex cuius clauis ferreis infixis ſingulis pla-<lb/>nis priſmatis, antliarum prementium emboli pendent, <lb/>atque ita quolibet eiusmodi librili, octo emboli pre-<lb/>mentes mouentur, de quibus actum eſt §. </s>
  <s xml:id="echoid-s270" xml:space="preserve">8. </s>
  <s xml:id="echoid-s271" xml:space="preserve">Libra-<lb/>men autem modo in plano eodem uerticali cum <lb/>cruce, modo in alio ad hanc normali collocari poſſe, <lb/>prout ſpatii ratio permittit, euidens omnino eſt, et ex-<lb/>emplum habet pars figurae ſiniſtra, num. </s>
  <s xml:id="echoid-s272" xml:space="preserve">I.</s>
  <s xml:id="echoid-s273" xml:space="preserve"/>
</p>
<div xml:id="echoid-div10" type="float" level="2" n="3">
<note position="right" xlink:label="note-0023-01" xlink:href="note-0023-01a" xml:space="preserve">Fig. VIII. <lb/>Tab. I.</note>
</div>
<p>
  <s xml:id="echoid-s274" xml:space="preserve">16. </s>
  <s xml:id="echoid-s275" xml:space="preserve">Praeterea alterutri ligno pendulo ferrum longi-<lb/>us infixum eſt, quo embolus antliae aſpirantis firmatur, <lb/>qua quippe nutriuntur ſiue humectantur coria antlia-<lb/>rum prementium. </s>
  <s xml:id="echoid-s276" xml:space="preserve">v. </s>
  <s xml:id="echoid-s277" xml:space="preserve">§. </s>
  <s xml:id="echoid-s278" xml:space="preserve">8. </s>
  <s xml:id="echoid-s279" xml:space="preserve">Eum in finem ſumma ant-<lb/>liarum laudatarum ora deſinunt in fundo receptaculi <lb/>plumbei, in quod effunduntur aquae eleuatae. </s>
  <s xml:id="echoid-s280" xml:space="preserve">Hoc <lb/>receptaculum diſſectum etiam ſiſtitur Fig. </s>
  <s xml:id="echoid-s281" xml:space="preserve">7. </s>
  <s xml:id="echoid-s282" xml:space="preserve">num. </s>
  <s xml:id="echoid-s283" xml:space="preserve">14. <lb/></s>
  <s xml:id="echoid-s284" xml:space="preserve">unacum trabe, qua nititur, interim tamen ad diſtinctio-<lb/>rem rei repraeſentationem adieci ichnographiam
<pb o="14" file="0024" n="24" rhead="CAPVT I."/>
Fig. </s>
  <s xml:id="echoid-s285" xml:space="preserve">6. </s>
  <s xml:id="echoid-s286" xml:space="preserve">in qua, a, b, c, d, ſunt oſtia quatuor antliarum <lb/>prementium, e patens os antliae aſpirantis. </s>
  <s xml:id="echoid-s287" xml:space="preserve">et quadra-<lb/>tum in medio notat foramen receptaculi, per quod <lb/>medium inter embolos quatuor lignum priſmaticum, <lb/>quod ueluti embolos hoſce dirigit, aſcendit et deſcen-<lb/>dit. </s>
  <s xml:id="echoid-s288" xml:space="preserve">Cum enim ſcapi embolorum ferrei ſint, qui uio-<lb/>lenta preſſione uacillare, et in obliquum ſitum torque-<lb/>ri poterant, his incommodis tignum ſolidum, et eius <lb/>motus per aptatum ipſi foramen, iuxta quod praeter-<lb/>ea’ aliae trabes iacent, accurate obuiam ire uidetur.</s>
  <s xml:id="echoid-s289" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s290" xml:space="preserve">17. </s>
  <s xml:id="echoid-s291" xml:space="preserve">Cylindrus quilibet antliae prementis habet dia-<lb/>metrum 6 {1/2} dig. </s>
  <s xml:id="echoid-s292" xml:space="preserve">cuiuis, ut ſupra dixi, reſpondet fiſtula <lb/>aſpirans plumbea diam. </s>
  <s xml:id="echoid-s293" xml:space="preserve">3 dig. </s>
  <s xml:id="echoid-s294" xml:space="preserve">alta 13 p. </s>
  <s xml:id="echoid-s295" xml:space="preserve">cum collo cu-<lb/>preo, quae in aquarum torrentem demiſſa, oſtio ſuo <lb/>recuruo aquas haurit, et atmoſphaerici ponderis auxi-<lb/>lio attollit. </s>
  <s xml:id="echoid-s296" xml:space="preserve">tanta autem celeritate tantaque uehementia <lb/>aquae per hunc tubum aſſurgunt, ut ſaepe piſciculi una <lb/>aſcendant. </s>
  <s xml:id="echoid-s297" xml:space="preserve">Motus emboli fit in perpendiculo 4 {1/2} p. </s>
  <s xml:id="echoid-s298" xml:space="preserve">et <lb/>tantundem aquae uno hauſtu antlia recipit et extrudit. <lb/></s>
  <s xml:id="echoid-s299" xml:space="preserve">Antliae etiam cuiuis tubus aptatus eſt, intra quem in-<lb/>truduntur aquae, et ad ſuperiora caſtella deferuntur. </s>
  <s xml:id="echoid-s300" xml:space="preserve"><lb/>interim tamen plures mox in unum coeunt, et tantum <lb/>quinque ampliores, diam. </s>
  <s xml:id="echoid-s301" xml:space="preserve">8. </s>
  <s xml:id="echoid-s302" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s303" xml:space="preserve">ad caſtella media, tres <lb/>nempe ad caſtellum ſiniſtrum, duo ad dextrum per-<lb/>ueniunt.</s>
  <s xml:id="echoid-s304" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s305" xml:space="preserve">18. </s>
  <s xml:id="echoid-s306" xml:space="preserve">Rotarum manubria ferrea, quae celeriorem mo-<lb/>tum habent, intra aeneas matrices gyrantur, ne incen-<lb/>dium efficiant. </s>
  <s xml:id="echoid-s307" xml:space="preserve">dicuntur etiam minus atteri, cum intra <lb/>aes mouentur. </s>
  <s xml:id="echoid-s308" xml:space="preserve">multum autem facit ad impedienda in-<lb/>cendia deſtillatio aquarum perpetua a rotae alis.</s>
  <s xml:id="echoid-s309" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s310" xml:space="preserve">19. </s>
  <s xml:id="echoid-s311" xml:space="preserve">Secundum rotarum officium ſpectat ad trahen-<lb/>das catenas parallelas, quarum nonnullae plusquam <lb/>ducentarum ſexpedarum longitudinem habent. </s>
  <s xml:id="echoid-s312" xml:space="preserve">Iterum
<pb o="15" file="0025" n="25" rhead="DE MACHINA MARLYENSI."/>
hic crux ſiue norma horizontalis lignea adhibetur, <lb/>quam explicationis cauſa in Fig. </s>
  <s xml:id="echoid-s313" xml:space="preserve">8. </s>
  <s xml:id="echoid-s314" xml:space="preserve">Tab. </s>
  <s xml:id="echoid-s315" xml:space="preserve">2. </s>
  <s xml:id="echoid-s316" xml:space="preserve">paululum <lb/>eleuatam delineaui. </s>
  <s xml:id="echoid-s317" xml:space="preserve">Scilicet manubrium curuatum A, <lb/>apprehendit tignum AB, circiter 9 pedes longum, quod <lb/>extremo ſuo mouet tignum alterum BC, 16. </s>
  <s xml:id="echoid-s318" xml:space="preserve">p. </s>
  <s xml:id="echoid-s319" xml:space="preserve">ab axe <lb/>medio intra trabes fortes ſuſpenſum, et in uerticem li-<lb/>bratum. </s>
  <s xml:id="echoid-s320" xml:space="preserve">huic adhaeret tignum horizontale CD, ſimilis <lb/>fere cum libramento longitudinis, quod connexum <lb/>eſt, cum extremo perpendiculi D, crucis horizontalis <lb/>EFD, in medio circa clauum rotundum mobilis. </s>
  <s xml:id="echoid-s321" xml:space="preserve">tan-<lb/>dem in puncto tranſuerſae trabis huius crucis F adhae-<lb/>ret catena FG, quae non flexilis eſt, uti in tr. </s>
  <s xml:id="echoid-s322" xml:space="preserve">Ioncherii <lb/>p. </s>
  <s xml:id="echoid-s323" xml:space="preserve">156. </s>
  <s xml:id="echoid-s324" xml:space="preserve">pingitur, uerum componitur ex longuriis ferreis <lb/>quadrilateris, longis plerumque 12 uel 15 p. </s>
  <s xml:id="echoid-s325" xml:space="preserve">lat. </s>
  <s xml:id="echoid-s326" xml:space="preserve">3 dig. <lb/></s>
  <s xml:id="echoid-s327" xml:space="preserve">ſpiſſ. </s>
  <s xml:id="echoid-s328" xml:space="preserve">1. </s>
  <s xml:id="echoid-s329" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s330" xml:space="preserve">et ferrum ſuperius FG copulatur cum ex-<lb/>tremo fortioris tigni in plano uerticali ſuſpenſi, quod <lb/>infra aliam ſimilem catenam ſuperiori parallelam tra-<lb/>hit, atque ita tandem motus oſcillationis in caſtella us-<lb/>que ſuperiora continuatur.</s>
  <s xml:id="echoid-s331" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s332" xml:space="preserve">20. </s>
  <s xml:id="echoid-s333" xml:space="preserve">Haec ut clarius pateant, ſequentia inſuper, de <lb/>
<anchor type="note" xlink:label="note-0025-01a" xlink:href="note-0025-01"/>
cruce, tignis in uerticem conuerſis, et catenis addam. <lb/></s>
  <s xml:id="echoid-s334" xml:space="preserve">crux fere eandem cum horizontali habet magnitudi-<lb/>nem, niſi quod brachium otioſum E minus eſſe poſſit, <lb/>alterum uero KF minimum 6 p. </s>
  <s xml:id="echoid-s335" xml:space="preserve">eſſe debet. </s>
  <s xml:id="echoid-s336" xml:space="preserve">tigna oſcillan-<lb/>tia (gall. </s>
  <s xml:id="echoid-s337" xml:space="preserve">balanciers) duplicis ſunt generis. </s>
  <s xml:id="echoid-s338" xml:space="preserve">fortiora, quae <lb/>etiam ſubſidiaria uel firmamenta (renforts) uocantur, <lb/>quale in figura 10, literis GG ſignificatur, horum claui in <lb/>extremis penetrant longurios ferreos ſiue catenas, adeo-<lb/>que efficiunt, ut motui rotae obſequantur. </s>
  <s xml:id="echoid-s339" xml:space="preserve">tales in machi-<lb/>na 1500 numerari, relatum mihi eſt. </s>
  <s xml:id="echoid-s340" xml:space="preserve">alterum genus con-<lb/>ſtituunt tigna tenuiora itidem clauis inſtructa in extre-<lb/>mis, quibus incumbunt catenae, adeoque tantum <lb/>portant longurios ferreos, et impediunt eorum curua-
<pb o="16" file="0026" n="26" rhead="CAPVT I."/>
tionem. </s>
  <s xml:id="echoid-s341" xml:space="preserve">talia conſpiciuntur plura fig. </s>
  <s xml:id="echoid-s342" xml:space="preserve">10. </s>
  <s xml:id="echoid-s343" xml:space="preserve">num. </s>
  <s xml:id="echoid-s344" xml:space="preserve">2. </s>
  <s xml:id="echoid-s345" xml:space="preserve">2. </s>
  <s xml:id="echoid-s346" xml:space="preserve">2. </s>
  <s xml:id="echoid-s347" xml:space="preserve">2. <lb/></s>
  <s xml:id="echoid-s348" xml:space="preserve">Longitudo tignorum eadem eſt, nempe 13 p. </s>
  <s xml:id="echoid-s349" xml:space="preserve">prope <lb/>uiam tamen, qua S. </s>
  <s xml:id="echoid-s350" xml:space="preserve">Germanum itur, paululum ſunt <lb/>contractiora, quia inferiora fulcimentorum extrema, <lb/>a uia 12 pedib. </s>
  <s xml:id="echoid-s351" xml:space="preserve">extollenda erant, ut curribus infra cate-<lb/>nas liber tranſitus relinqueretur. </s>
  <s xml:id="echoid-s352" xml:space="preserve">Repetuntur ligna <lb/>minora ſiue tenuiora, interuallo 16 pedum, ut pluri-<lb/>mum; </s>
  <s xml:id="echoid-s353" xml:space="preserve">maiora 8 uel 10 ſexpedis inuicem diſtant. </s>
  <s xml:id="echoid-s354" xml:space="preserve">Ca-<lb/>tenarum longurii longitudinem 15 uel 16 p. </s>
  <s xml:id="echoid-s355" xml:space="preserve">habent. </s>
  <s xml:id="echoid-s356" xml:space="preserve"><lb/>miſcentur iis nonnunquam membra parua bipedalia, <lb/>N, N. </s>
  <s xml:id="echoid-s357" xml:space="preserve">fig. </s>
  <s xml:id="echoid-s358" xml:space="preserve">10. </s>
  <s xml:id="echoid-s359" xml:space="preserve">quae catenae fractae (Chaines brifées) nun-<lb/>cupantur, et ſeruiunt fabris, ad cognoſcendas catenas <lb/>ruptas. </s>
  <s xml:id="echoid-s360" xml:space="preserve">ſiquidem cum alicubi longurius rumpitur, ca-<lb/>tenae hae paruae non rigide trahuntur, et ſic incuruan-<lb/>tur earum membra, quae alias, integris longuriis ab utra-<lb/>que parte, eandem cum iis lineam rectam ſeruant. </s>
  <s xml:id="echoid-s361" xml:space="preserve">Ca-<lb/>tenarum prima portio FG fig. </s>
  <s xml:id="echoid-s362" xml:space="preserve">8. </s>
  <s xml:id="echoid-s363" xml:space="preserve">nonnunquam longius <lb/>in ipſa machina continuanda eſt, quemadmodum et-<lb/>iam ex fig. </s>
  <s xml:id="echoid-s364" xml:space="preserve">1. </s>
  <s xml:id="echoid-s365" xml:space="preserve">intelligitur, atque eo caſu ſupponuntur <lb/>cylindri ferris planis ueſtiti, quibus ſuſtentantur lon-<lb/>gurii, ut recti perpetuo exiſtant. </s>
  <s xml:id="echoid-s366" xml:space="preserve">Illud quoque ex ſu-<lb/>perioribus conſequitur, quod ope crucis repetitae, ca-<lb/>tenarum longurii uarie flecti, itemque attolli et deprimi <lb/>poſſint. </s>
  <s xml:id="echoid-s367" xml:space="preserve">Atque adeo haec artificia machinae Mar-<lb/>lyenſis uariis in caſibus utilitatem praeſtare pote-<lb/>runt.</s>
  <s xml:id="echoid-s368" xml:space="preserve"/>
</p>
<div xml:id="echoid-div11" type="float" level="2" n="4">
<note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">Fig. 8. <lb/>Tab. II.</note>
</div>
<p>
  <s xml:id="echoid-s369" xml:space="preserve">21. </s>
  <s xml:id="echoid-s370" xml:space="preserve">Supereſt, ut exponam, quomodo catenae mo-<lb/>ueant antlias caſtellorum ſuperiorum. </s>
  <s xml:id="echoid-s371" xml:space="preserve">Primum mo-<lb/>tum eſſiciunt, ante caſtellum ſiniſtrum, prope G, Fig. </s>
  <s xml:id="echoid-s372" xml:space="preserve">1. <lb/></s>
  <s xml:id="echoid-s373" xml:space="preserve">ibi enim in puteo colliguntur aquae fontium, ex uici-<lb/>nis montibus perriuos deriuatae, et cum eaedem pro-<lb/>pe caſtellum ipſum, ob eius altitudinem exonerari ne-<lb/>queant, puteo G impoſitae ſunt 28 antliae aſpirantes,
<pb o="17" file="0027" n="27" rhead="DE MACHINA MARLYENSI."/>
quarum agitatio antea a nemine diſtincte deſcripta eſt <lb/>delineaui hunc in finem figuram 9, in qua lineae 0000, <lb/>deſignant catenas parallelas, hae ut aquas ex puteo al-<lb/>tius attollant, ut deinceps lapſu naturali in caſtellum <lb/>ipſum profluant, impoſitae inferioribus trabibus ſunt co-<lb/>lumnae quaedam, ſiue fulcra ſuperioris contignationis. <lb/></s>
  <s xml:id="echoid-s374" xml:space="preserve">in hac GG trabs geſtat lignum FE et normam HKI, <lb/>quae circa clauos ſuos aguntur. </s>
  <s xml:id="echoid-s375" xml:space="preserve">primum parte altera <lb/>nectitur cum CA perpendiculo tigni ſubſidiarii, et ipſe <lb/>nexus craſſo ligno ED fit: </s>
  <s xml:id="echoid-s376" xml:space="preserve">parte altera F, ex ferreo <lb/>trunco emboli duo aſpirantes L, L, pendent. </s>
  <s xml:id="echoid-s377" xml:space="preserve">norma <lb/>autem HKI, mouetur ligno y, quod ſuper longurio <lb/>unco ferreo iacet, atque haec pars normae K modo <lb/>propellitur, modo attrahitur, eodemque motu agitan-<lb/>tur duo emboli MM, qui ex I dependent. </s>
  <s xml:id="echoid-s378" xml:space="preserve">Ita 28 ant-<lb/>liis diam. </s>
  <s xml:id="echoid-s379" xml:space="preserve">6. </s>
  <s xml:id="echoid-s380" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s381" xml:space="preserve">hauriuntur ex puteo aquae. </s>
  <s xml:id="echoid-s382" xml:space="preserve">motus em-<lb/>boli fit in perpendiculo 3 pedum, et aquae putei circi-<lb/>ter 20 pedib. </s>
  <s xml:id="echoid-s383" xml:space="preserve">a ſuperiori huius hauſtri receptaculo di-<lb/>ſtant. </s>
  <s xml:id="echoid-s384" xml:space="preserve">hinc per canalem plumbeum diam. </s>
  <s xml:id="echoid-s385" xml:space="preserve">1. </s>
  <s xml:id="echoid-s386" xml:space="preserve">ped. </s>
  <s xml:id="echoid-s387" xml:space="preserve">deſcen-<lb/>dunt, et ad caſtellum ſiniſtrum deuoluuntur.</s>
  <s xml:id="echoid-s388" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s389" xml:space="preserve">22. </s>
  <s xml:id="echoid-s390" xml:space="preserve">Neque tamen aquae ſtatim in ipſum caſtello ſub-<lb/>iectum puteum illabuntur, ſed deriuantur fiſtulis, in <lb/>commune receptaculum ſiue ſtagnum H, Fig. </s>
  <s xml:id="echoid-s391" xml:space="preserve">1. </s>
  <s xml:id="echoid-s392" xml:space="preserve">atque <lb/>inde puriores redeunt. </s>
  <s xml:id="echoid-s393" xml:space="preserve">Eodem recipiuntur, quae per <lb/>aquae ductum ex opere ſtructili, et a uilla Selle per 1200 <lb/>ſexpedas continuatum, lat. </s>
  <s xml:id="echoid-s394" xml:space="preserve">2 p. </s>
  <s xml:id="echoid-s395" xml:space="preserve">alt. </s>
  <s xml:id="echoid-s396" xml:space="preserve">3 {1/2} prope caſtellum <lb/>ſiniſtrum effunduntur.</s>
  <s xml:id="echoid-s397" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s398" xml:space="preserve">23. </s>
  <s xml:id="echoid-s399" xml:space="preserve">In caſtellis mediis, quorum ſaepe feci mentionem, <lb/>hauriuntur aquae ulterius antliis inuerſis, quarum actio-<lb/>nem fig. </s>
  <s xml:id="echoid-s400" xml:space="preserve">10. </s>
  <s xml:id="echoid-s401" xml:space="preserve">clare ob oculos ponit. </s>
  <s xml:id="echoid-s402" xml:space="preserve">nimirum crux AB <lb/>apprehenditur a catena ſuperiore in F, et ex A pendent <lb/>ex ferris longis, ita ut figura docet compactis, tres qua-<lb/>tuorue emboli inuerſi, intra cylindros, quorum imum os
<pb o="18" file="0028" n="28" rhead="CAPVT I."/>
aquis putei immerſum eſt, atque ita, uti §. </s>
  <s xml:id="echoid-s403" xml:space="preserve">9. </s>
  <s xml:id="echoid-s404" xml:space="preserve">deſcripſi <lb/>uberius, premuntur et truduntur aquae in ſuperiores fi-<lb/>ſtulas, quae cylindris antliarum affixae ſunt. </s>
  <s xml:id="echoid-s405" xml:space="preserve">Similiter in-<lb/>ferior catena FH ducit normam FED, cui ex E adhae-<lb/>rent tres emboli inuerſi, qui eodem officio quo priores <lb/>funguntur. </s>
  <s xml:id="echoid-s406" xml:space="preserve">Emboli autem hi inuerſi, ex transuerſis fer-<lb/>reis ſuſtentaculis ſic ſuſpenſi ſunt, ut exemto clauo ſin-<lb/>guli demi iterumque addi queant, ut non ſolum em-<lb/>bolorum uitia, ſi qua ſunt, corrigantur, u. </s>
  <s xml:id="echoid-s407" xml:space="preserve">§. </s>
  <s xml:id="echoid-s408" xml:space="preserve">10, ſed <lb/>etiam ut onus augeatur uel minuatur, prouti rotae ma-<lb/>iore minoriue impetu gyrantur. </s>
  <s xml:id="echoid-s409" xml:space="preserve">In ſiniſtro igitur ca-<lb/>ſtello, in quo ſeptem catenae deſinunt, quadraginta <lb/>nouem antliae inuerſae moueri poſſunt, dum ſingulis <lb/>catenarum paribus ſeptem emboli trahuntur. </s>
  <s xml:id="echoid-s410" xml:space="preserve">Nam <lb/>tantum hae catenae onerantur, quantum facultatis mo-<lb/>uentis impetus fert, quia earum uſus ulterius non ex-<lb/>tenditur. </s>
  <s xml:id="echoid-s411" xml:space="preserve">Verum in ſiniſtro paulo aliter ſeſe res ha-<lb/>bet. </s>
  <s xml:id="echoid-s412" xml:space="preserve">hic enim tantum catenae alternae, modo ſuperio-<lb/>res modo inferiores embolos ducunt, in 40 antliis, et <lb/>ordinarie tantum duo emboli e catenis ſingulis pen-<lb/>dent. </s>
  <s xml:id="echoid-s413" xml:space="preserve">ut iſtae oneribus in ſupremis antliis tollendis <lb/>propellendisque ſufficiant. </s>
  <s xml:id="echoid-s414" xml:space="preserve">Tubi antliarum habent <lb/>diametrum 6 {1/2} dig. </s>
  <s xml:id="echoid-s415" xml:space="preserve">rectangula embolorum 15 p. </s>
  <s xml:id="echoid-s416" xml:space="preserve">longa <lb/>ſunt, et motus horum intra 4 p. </s>
  <s xml:id="echoid-s417" xml:space="preserve">contingit.</s>
  <s xml:id="echoid-s418" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s419" xml:space="preserve">24. </s>
  <s xml:id="echoid-s420" xml:space="preserve">Fiſtulae ex mediis puteis aquas prope ſum-<lb/>mum caſtellum ducentes ſequentes ſunt. </s>
  <s xml:id="echoid-s421" xml:space="preserve">Quinque <lb/>diam. </s>
  <s xml:id="echoid-s422" xml:space="preserve">6 dig. </s>
  <s xml:id="echoid-s423" xml:space="preserve">egrediuntur ex ſiniſtro, qui tandem in <lb/>tres diametri 8 dig. </s>
  <s xml:id="echoid-s424" xml:space="preserve">congregantur, et in receptaculo L <lb/>finiuntur. </s>
  <s xml:id="echoid-s425" xml:space="preserve">ex dextro autem caſtello duae tantum fiſtu-<lb/>lae parallelae procedunt diam. </s>
  <s xml:id="echoid-s426" xml:space="preserve">8 dig.</s>
  <s xml:id="echoid-s427" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s428" xml:space="preserve">25. </s>
  <s xml:id="echoid-s429" xml:space="preserve">Tam inſignem aquarum copiam, quae in ſupre-<lb/>mi caſtelli puteum ingeritur, tandem antliae octua-<lb/>ginta duae ulterius hauriunt, et receptaculo, quod in
<pb o="19" file="0029" n="29" rhead="DE MACHINA MARLYENSI."/>
principio aquaeductus eſt, tradunt. </s>
  <s xml:id="echoid-s430" xml:space="preserve">quaeuis catena <lb/>tantum tres embolos agitat, exceptis quatuor, quibus <lb/>totidem emboli annexi ſunt. </s>
  <s xml:id="echoid-s431" xml:space="preserve">ut figura 10 indicat, quae <lb/>ſiſtit orthographiam interiorem caſtelli ſupremi. </s>
  <s xml:id="echoid-s432" xml:space="preserve">Ant-<lb/>liae et emboli ſimilem cum inferioribus conditionem <lb/>habent, aquae in puteum per canales admittuntur, quo-<lb/>rum oſtia cochleis adduci et demitti, et ſic aperiri at-<lb/>que claudi poſſunt. </s>
  <s xml:id="echoid-s433" xml:space="preserve">ante hoc caſtellum eſt puteus O <lb/>Fig. </s>
  <s xml:id="echoid-s434" xml:space="preserve">1, in quem influunt aquae periturae, et ex eo ite-<lb/>rum aliquot antliis aſpirantibus hauriuntur, applicatis <lb/>nempe normalibus lignis, ad oſcillantia, quae ſuperius <lb/>ſubſidiaria nominauimus.</s>
  <s xml:id="echoid-s435" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s436" xml:space="preserve">26. </s>
  <s xml:id="echoid-s437" xml:space="preserve">Exeunt ex hoc caſtello fiſtulae ferreae tredecim, <lb/>diam. </s>
  <s xml:id="echoid-s438" xml:space="preserve">6. </s>
  <s xml:id="echoid-s439" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s440" xml:space="preserve">et abhinc circiter interuallo 14 ſexpeda-<lb/>rum, in ſex alias fiſtulas, quarum diam. </s>
  <s xml:id="echoid-s441" xml:space="preserve">8 digitos capit, <lb/>coeunt, factis in extremis furcarum ualuulis. </s>
  <s xml:id="echoid-s442" xml:space="preserve">Haec au-<lb/>tem deductio in nouos tubos neceſſaria fuit, ut omnis <lb/>aer excludatur, et preſſio aquarum commodius fieret. <lb/></s>
  <s xml:id="echoid-s443" xml:space="preserve">Abeſt turris aquaeductus ab hoc caſtello 290 perticis ſex-<lb/>pedalibus. </s>
  <s xml:id="echoid-s444" xml:space="preserve">Perpendicula aquarum libellatione usque ad <lb/>receptaculum aquaeductus reperta ſunt ſequentia. </s>
  <s xml:id="echoid-s445" xml:space="preserve">flu-<lb/>men caſtellis mediis humilius eſt 148 pedibus. </s>
  <s xml:id="echoid-s446" xml:space="preserve">hinc ca-<lb/>ſtellum ſupremum altius eſt 175 p. </s>
  <s xml:id="echoid-s447" xml:space="preserve">tandemque recepta-<lb/>culum aquaeductus editius eſt 177 pedibus. </s>
  <s xml:id="echoid-s448" xml:space="preserve">quibus in <lb/>ſummam collectis, conficitur perpendiculum 500 pe-<lb/>dum regiorum, per quod aſſurgunt aquae a flumine <lb/>in aquaeductum.</s>
  <s xml:id="echoid-s449" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s450" xml:space="preserve">27. </s>
  <s xml:id="echoid-s451" xml:space="preserve">Nimirum cum ad turrim aquaeductus appro-<lb/>pinquant fiſtulae, applicantur ferreis plumbeae eius-<lb/>dem diametri 8 dig. </s>
  <s xml:id="echoid-s452" xml:space="preserve">colli modicum accliui incumben-<lb/>tes, et per has tandem aſcendunt aquae in receptacu-<lb/>lum aquaeductus ſubdiale plumbeum, quod ſuper ta-<lb/>bulato firmiter tignis quernis fabricato requieſcit, fi-
<pb o="20" file="0030" n="30" rhead="CAPVT I."/>
guram quadratam lateris 12 p. </s>
  <s xml:id="echoid-s453" xml:space="preserve">et profunditatem 3 p-<lb/>habens. </s>
  <s xml:id="echoid-s454" xml:space="preserve">Turris autem cum lorica 96 p. </s>
  <s xml:id="echoid-s455" xml:space="preserve">alta eſt, et ad <lb/>receptaculum aquarum ſcala 123 graduum, qui ſinguli <lb/>9 dig. </s>
  <s xml:id="echoid-s456" xml:space="preserve">alti ſunt, peruenitur. </s>
  <s xml:id="echoid-s457" xml:space="preserve">Aquaeductus ipſe ex ſo-<lb/>lido muro factus 330 ſexpedas longus, arcubus 36 di-<lb/>ſtinguitur. </s>
  <s xml:id="echoid-s458" xml:space="preserve">canalis, ſiue riuus, in quo aquae ſupra arcum <lb/>deuoluuntur, plumbo ueſtitus, 3 p. </s>
  <s xml:id="echoid-s459" xml:space="preserve">latus, et fornix qui <lb/>eum claudit 4 {1/2} p. </s>
  <s xml:id="echoid-s460" xml:space="preserve">altus, lapidibusque quadratis probe <lb/>tectus eſt. </s>
  <s xml:id="echoid-s461" xml:space="preserve">Muri ſpiſſitudo prope terram 18 p. </s>
  <s xml:id="echoid-s462" xml:space="preserve">in ſupe-<lb/>riore parte 6 p. </s>
  <s xml:id="echoid-s463" xml:space="preserve">exiſtit.</s>
  <s xml:id="echoid-s464" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s465" xml:space="preserve">28. </s>
  <s xml:id="echoid-s466" xml:space="preserve">In altero aquaeductus extremo turris alia humi-<lb/>lior anguſtiorque conſiſtit, cuius receptaculum 47 ped. <lb/></s>
  <s xml:id="echoid-s467" xml:space="preserve">a ſolo remouetur, et ab eodem duae fiſtulae ferreae, <lb/>diam. </s>
  <s xml:id="echoid-s468" xml:space="preserve">18 dig. </s>
  <s xml:id="echoid-s469" xml:space="preserve">demittuntur, per quas aqua in recepta-<lb/>cula Marlyenſia, quae a turri ultima 350 ſexpedis di-<lb/>ſtant, labitur, et inde iterum tum in gradus, ex quibus <lb/>praeceps ruit, (caſcades) tum in fonticulos, circum <lb/>et infra arcem regiam factos, deriuatur. </s>
  <s xml:id="echoid-s470" xml:space="preserve">Olim haec <lb/>aqua Verſalias per ſtructiles canales in craterem ſiue ca-<lb/>ſtellum aquarum ingens, quod in extremo arcis angu-<lb/>lo eſt, profluebat, uerum hodie portio praecipua in <lb/>hortos Marlyacenſes ducitur, poſtquam collectae riuis <lb/>in montibus uicinis aquae, ſuper Montrelienſem <lb/>aquaeductum nouum, Verſalias in caſtellum pe-<lb/>culiare, (chateau d’eau) et inde in ampliſſimum <lb/>receptaculum antea commemoratum deriuantur. </s>
  <s xml:id="echoid-s471" xml:space="preserve"><lb/>Caſtellum, cuius modo memini eſt ahenum <lb/>amplisſimum, intra aedes peculiares, e regione rece-<lb/>ptaculi magni exſtructas, contignationi quernis trabi-<lb/>bus factae impoſitum, ſupra horizontalem lineam ad <lb/>altitudinem perpendicularem ſexaginta ſex pedum ele-<lb/>uatum, et ſeptem pedum profunditatem habens. </s>
  <s xml:id="echoid-s472" xml:space="preserve">A-<lb/>quae per aquaeductum montrelienſem huc aduectae,
<pb o="21" file="0031" n="31" rhead="DE MACHINA MARLYENSI."/>
iterum per fiftulas cupreas delabuntur, et in receptacu-<lb/>lum magnum (grand reſervoir) perueniunt. </s>
  <s xml:id="echoid-s473" xml:space="preserve">Hoc re-<lb/>ceptaculum quadratum muro clauſum, et ſpatium in-<lb/>tra muros terra repletum eſt, cui incumbit in ſummo <lb/>ſtratum argilloſum, tres pedes altum, et pauimento <lb/>tectum. </s>
  <s xml:id="echoid-s474" xml:space="preserve">Quin etiam murus undique argilla ſuperiore <lb/>parte ueſtitus eſt, ut aquas rectius contineat. </s>
  <s xml:id="echoid-s475" xml:space="preserve">Ex hoc <lb/>pauimento deorſum deductae ſunt fiſtulae plumbeae, <lb/>operculo cupreo perforato tectae, (quod purgandis <lb/>aquis feruit,) per quas ad inſtruendos in horto fonti-<lb/>culos, quorum miranda ibidem uarietas eſt, aquae ite-<lb/>rum deſcendunt.</s>
  <s xml:id="echoid-s476" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s477" xml:space="preserve">29. </s>
  <s xml:id="echoid-s478" xml:space="preserve">Ex hac luculentiore uaſti operis deſcriptione in-<lb/>telligi aliquantum tum magnitudo eius, tum praeſtan-<lb/>tia poteſt. </s>
  <s xml:id="echoid-s479" xml:space="preserve">Poſterior magis adhuc illuſtrabitur, ubi di-<lb/>xerimus de copia aquarum, quas attollit. </s>
  <s xml:id="echoid-s480" xml:space="preserve">priorem <lb/>quisque colligat licet, ex membrorum, quibus conſtat, <lb/>numero, et ex materiae, quae in illam impenſa eſt, mo-<lb/>le. </s>
  <s xml:id="echoid-s481" xml:space="preserve">refertur enim, conſumtas in eius conſtructione fuiſſe <lb/>1700000 libras cupri, totidem libras plumbi, ferri ma-<lb/>teriam cuprum uigeſies, lignum idem centies excede-<lb/>re. </s>
  <s xml:id="echoid-s482" xml:space="preserve">antlias continet aſpirantes 44, prementes 64, inuer-<lb/>fas 161; </s>
  <s xml:id="echoid-s483" xml:space="preserve">et cum exſtrueretur, 1800 homines per annos <lb/>ſeptem continuo in eadem elaboranda operam pro-<lb/>fuerunt. </s>
  <s xml:id="echoid-s484" xml:space="preserve">Et hodie ob ingentem partium multitudi-<lb/>nem, eidem cuſtodiendae et reficiendae praeſunt 60 <lb/>operarii, aquileges, fuſores, fabrique, inſpectoribus ex-<lb/>ceptis, et 9 ex iis quauis nocte prope machinam et in <lb/>caſtellis excubias agunt, atque adeo eius conſeruatio <lb/>ſine maximis ſumtibus fieri nequit.</s>
  <s xml:id="echoid-s485" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s486" xml:space="preserve">30. </s>
  <s xml:id="echoid-s487" xml:space="preserve">Ob uarietatem autem eorum, quae hic a curio-<lb/>ſo ſpectatore obſeruanda ſunt, non eſt tam expeditum, <lb/>tantae molis ideam, breui, etiam cum quis praeſens eſt,
<pb o="22" file="0032" n="32" rhead="CAPVT I."/>
animo concipere. </s>
  <s xml:id="echoid-s488" xml:space="preserve">quam ob rem ſcribit, <emph style="sc">Pignial de <lb/>la</emph> <emph style="sc">Force</emph> dans la nouvelle deſcription des chateaux et <lb/>Parc de Verſailles et de Marly, Tom. </s>
  <s xml:id="echoid-s489" xml:space="preserve">2. </s>
  <s xml:id="echoid-s490" xml:space="preserve">p. </s>
  <s xml:id="echoid-s491" xml:space="preserve">259. </s>
  <s xml:id="echoid-s492" xml:space="preserve">La groſſeur de <lb/>ce Volume ſuffiroit à peine pour decrire la conſtruction, les mou-<lb/>vemens et les effets de la machine de Marly. </s>
  <s xml:id="echoid-s493" xml:space="preserve">Peu de gens ſont <lb/>d’ ailleurs capables de les comprendre, puisque Mr. </s>
  <s xml:id="echoid-s494" xml:space="preserve">de Ville <lb/>aſſure, qu’il n’a presque trouvé, que feu Mr. </s>
  <s xml:id="echoid-s495" xml:space="preserve">le Marechal de <lb/>Vauban, qui en voyantce merveilleux ouvrage en ait connû la <lb/>plûpart des effets. </s>
  <s xml:id="echoid-s496" xml:space="preserve">ſi quis uero iam ante lectione deſcri-<lb/>ptionis huius mentem praeparauerit, et alias hydrau-<lb/>licorum elementorum non prorſus ignarus ſit, putem <lb/>eum clariſſime uidere poſſe, qualis cuiusque membri in <lb/>machina conſtructio et uſus exiſtat. </s>
  <s xml:id="echoid-s497" xml:space="preserve">Quin etiam re-<lb/>motus a machina, cum haecleget, eundem ſcopum aſſe-<lb/>qui ualeat, minime dubito, et huic finitotam explica-<lb/>tionem ſolicite accommodaui. </s>
  <s xml:id="echoid-s498" xml:space="preserve">Ceterum ut ſpeci-<lb/>men habeatur deſcriptionis eiusmodi, qualis Pariſiis <lb/>cum imaginibus machinae Marlyenſis uenditur, in-<lb/>ſeram compendioſam uaſti operis explicationem, <lb/>quam a Nicol. </s>
  <s xml:id="echoid-s499" xml:space="preserve">de Fer caelatore Pariſienſi accepi, cu-<lb/>ius ſaltem ille uſus eſſe poteſt, ut quis generalem ma-<lb/>chinae, de qua loquor, ideam animo complectatur. <lb/></s>
  <s xml:id="echoid-s500" xml:space="preserve">Deſcription de la machine de Marly, qui conduiſit lex eaux a <lb/>Verſailles. </s>
  <s xml:id="echoid-s501" xml:space="preserve">on l’ appelle machine tout court, par l’ excellence, <lb/>elle eſt de l’ invention de Mr. </s>
  <s xml:id="echoid-s502" xml:space="preserve">le Chevalier de Ville, il a falu des <lb/>foreſts entieres pour faire la digue, et les galleries de char-<lb/>pente, qui ſont depuis la riviere de Seine, le long de la colline, <lb/>jusqu’ aut haut de la tour de pierre. </s>
  <s xml:id="echoid-s503" xml:space="preserve">Sous ces galleries ſont <lb/>par intervalles, ſur le terrain de la côte, les reſervoirs, les <lb/>uns ſuperieurs aux autres, le plus bas ayant reçû immediate-<lb/>ment l’ eau de la riviere, contient ſon corps de pompe, qui la <lb/>repouſſe par des tuyaux couchez le long de la colline, dans les <lb/>reſervoirs ſuperieurs, et ainſi par repriſe, jusqu’ au reſervoir,
<pb o="23" file="0033" n="33" rhead="DE MACHINA MARLYENSI."/>
qui eſt ſur la tour de pierre. </s>
  <s xml:id="echoid-s504" xml:space="preserve">les corps des pompes ont 4 pouces <lb/>de diametre, et quelques uns 6, et les piſtons par leur jeu de <lb/>4 pieds, apres avoir puiſ’e l’ eau, la refoulent, et la forcent à <lb/>monter dans les reſervoirs ſuperieurs. </s>
  <s xml:id="echoid-s505" xml:space="preserve">Tous ces mouvemens <lb/>ſe font par le moyen de cent balanciers vertic alement poſ’es, qui <lb/>ſont joints l’un à l’autre par les tirants, ausquels d’ autres <lb/>eſpeces de balanciers ſervent de ſupport, ainſi quand la partie <lb/>ſuperieure deſcend, les balanciers ſ’ epanchent vers lariviere, <lb/>et leurs parties inferieures remontant vers le haut de la colline, <lb/>tirent les piſtons, et puiſent l’ eau dans les corps des pompes, <lb/>d’ou ils larefoulent, lorsque la partie ſuperieure des balanciers <lb/>vient à remonter verticalement, et qu’elle ſ’incline vers le <lb/>baut de la colline. </s>
  <s xml:id="echoid-s506" xml:space="preserve">Le premier mobile de cette machine, eſt un <lb/>bras de lariviere de ſeine, qu’on a barré par une digue. </s>
  <s xml:id="echoid-s507" xml:space="preserve">Cette <lb/>digue eſt ouverte par deux endroits, par lesquels l’eau etant <lb/>retenuë, et plus elevée, et coulant avec rapidité, fait tourner <lb/>dans chaque pertuis, une rouë de 36 pieds de diametre, et <lb/>de 5 a 6 pieds de longueur d’ aisles. </s>
  <s xml:id="echoid-s508" xml:space="preserve">Les extremités des axes de <lb/>chaque rouë ſortent hors de leurs appuis, et ſont tournées en <lb/>manivelles. </s>
  <s xml:id="echoid-s509" xml:space="preserve">La manivelle qui eſt du coté de la montagne puiſe <lb/>et refoule l’eau dans les premiers corps de pompes, et l’autre <lb/>manivelle ſert à faire mouvoir les balanciers. </s>
  <s xml:id="echoid-s510" xml:space="preserve">Il y a 14 rouës, <lb/>neuf desquelles agiſſent ordinairement, et ſouvent les 14 toutes <lb/>enſembles, et fourniſſent 200 pouces d’ eau a Verſailles, en fai-<lb/>ſant mouvoir 2500 pieces de bois vertic alement, dont il n’y en a <lb/>que mille qui ſoient veritablement balanciers, les autres pieces <lb/>ne ſervent que de ſupport a leurs tirants, et toutes ces pieces <lb/>ne ſervent, qu’a faire mouvoir les mille balanciers, ou leviers, <lb/>lequels à chaque tour de rouë ſ’ inclinent d’ un coté et d’ autre, <lb/>et apres avoir retiré les piſtons des corps des pompes, qui re-<lb/>coivent une colonne d’ eau de 4 pieds de bauteur, et de 4 pou-<lb/>ces de diametre, la refoulent auſſitot. </s>
  <s xml:id="echoid-s511" xml:space="preserve">Treize de ces balanciers <lb/>ſont de front, et par lemoien de 62 autres, qui ſont le long de
<pb o="24" file="0034" n="34" rhead="CAPVT I."/>
la colline, ils ſeruent a puiſer l’eau du plus haut reſervoir <lb/>dans le corps des pompes, et à la refouler, et forcer par les <lb/>piſtons à monter dans les tuyaux verticalement poſés dans la <lb/>tour de pierre, et à degorger dans le reſervoir, qui eſt au plus <lb/>haut etage, d’ou l’eau deſcendant par d’ autres tuyaux, poſés à <lb/>plomb, et enfermez dans les tuyaux enterrez, vaſortir par des <lb/>tuyaux à plomb, dans le plus haut reſervoir duchateau de Ver-<lb/>ſailles, d’ ouelle eſt enſuite diſtribuée. </s>
  <s xml:id="echoid-s512" xml:space="preserve">Pour donner uneidée ap-<lb/>prochante de la grandeur de cette machine, il faut ſavoir, <lb/>qu’elle eleve les eaux, qu’elle fournit à Verſailles, de 83 Toi-<lb/>ſes de haut.</s>
  <s xml:id="echoid-s513" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s514" xml:space="preserve">31. </s>
  <s xml:id="echoid-s515" xml:space="preserve">De quantitate ſiue copia aquarum a machina in <lb/>aquaeductum propulſarum refert <emph style="sc">Force</emph> l. </s>
  <s xml:id="echoid-s516" xml:space="preserve">c. </s>
  <s xml:id="echoid-s517" xml:space="preserve">p. </s>
  <s xml:id="echoid-s518" xml:space="preserve">265. <lb/></s>
  <s xml:id="echoid-s519" xml:space="preserve">quod intra 24. </s>
  <s xml:id="echoid-s520" xml:space="preserve">horas effundat in receptacula Marlyenſia <lb/>tantum aquarum, quantum ſufficit, ad altitudinem 3 <lb/>digitor. </s>
  <s xml:id="echoid-s521" xml:space="preserve">in iisdem producendam, et hanc molem ca-<lb/>pere 779 ſexpedas cubicas, ſiue 21, 037 cados aquarum <lb/>(muids d’eau) qui ſinguli 280 menſuras uulgares ſiue <lb/>cantharos Pariſienſes, (pintes) qui cantharis Dreſden-<lb/>ſibus paululum ſunt maiores, complectuntur. </s>
  <s xml:id="echoid-s522" xml:space="preserve">adeoque <lb/>numerus cantharorum aquae, per diem integrum hau-<lb/>ſtorum, foret 5, 890, 360, eo quidem tempore, quan-<lb/>do flumen altum eſt, et cuncta machinae membra be-<lb/>ne ſeſe habent.</s>
  <s xml:id="echoid-s523" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s524" xml:space="preserve">32. </s>
  <s xml:id="echoid-s525" xml:space="preserve">Verum haec manifeſtius patebunt, rationibus <lb/>accuratius ſubductis. </s>
  <s xml:id="echoid-s526" xml:space="preserve">Sunt, ut ſupra retuli, in machi-<lb/>na ipſa 64 antliae prementes, quarum cylindri 6 dig. <lb/></s>
  <s xml:id="echoid-s527" xml:space="preserve">diametrum. </s>
  <s xml:id="echoid-s528" xml:space="preserve">embolus motum 4 p. </s>
  <s xml:id="echoid-s529" xml:space="preserve">habet. </s>
  <s xml:id="echoid-s530" xml:space="preserve">aſſurgunt igi-<lb/>tur in antliis 64 cylindri, datae altiludinis et baſeos, <lb/>factoque calculo efficitur, eorundem ſummae aequipol-<lb/>lere unum cylindrum aquae, qui 64 p. </s>
  <s xml:id="echoid-s531" xml:space="preserve">altus, 1 p. </s>
  <s xml:id="echoid-s532" xml:space="preserve">dia-<lb/>metrum habet, ſinguli autem cylindri, 1 p. </s>
  <s xml:id="echoid-s533" xml:space="preserve">alti, et 1 p. </s>
  <s xml:id="echoid-s534" xml:space="preserve"><lb/>diametri, habent pondus 55 librarum, uid. </s>
  <s xml:id="echoid-s535" xml:space="preserve"><emph style="sc">Ionche-</emph>
<pb o="25" file="0035" n="35" rhead="DE MACHINA MARLYENSI."/>
<emph style="sc">RIVS</emph> intr. </s>
  <s xml:id="echoid-s536" xml:space="preserve">gall. </s>
  <s xml:id="echoid-s537" xml:space="preserve">cuititulus; </s>
  <s xml:id="echoid-s538" xml:space="preserve">Nouvelle methode de forti-<lb/>fierles plus grandes uilles, ſuiuie de diſſertations ſur la <lb/>machine de Marly et ſur les Pompes du Pont de Notre-<lb/>Dame etc. </s>
  <s xml:id="echoid-s539" xml:space="preserve">Pariſ. </s>
  <s xml:id="echoid-s540" xml:space="preserve">1718 in 12. </s>
  <s xml:id="echoid-s541" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s542" xml:space="preserve">p. </s>
  <s xml:id="echoid-s543" xml:space="preserve">148. </s>
  <s xml:id="echoid-s544" xml:space="preserve">qui tamen non ad-<lb/>dit rationem, quae ab experimentis peti debet, quibus <lb/>conſtitit, pedem cubicum aquae fluminis ponderi 70 li-<lb/>brarum aequipollere, et quia cubus ad cylindrum ae-<lb/>que altum habet rationem quam quadratum ad circulum, <lb/>ſi inferas 14: </s>
  <s xml:id="echoid-s545" xml:space="preserve">11 = 70: </s>
  <s xml:id="echoid-s546" xml:space="preserve">55 inuenies aſſerti ueritatem. </s>
  <s xml:id="echoid-s547" xml:space="preserve">ita-<lb/>que 64, continent 3520 libras, ſiue 1760 cantharos Pa-<lb/>riſienſes. </s>
  <s xml:id="echoid-s548" xml:space="preserve">Praeterea experientia confirmauit, rotas <lb/>uno temporis minuto bis gyrari, quando flumen plus-<lb/>quam mediocri impetu fertur, ergo 3520 menſurae ſiue <lb/>canthari Pariſienſes, intra minutum temporis, cum ma-<lb/>chinaenihil deeſt, extolluntur: </s>
  <s xml:id="echoid-s549" xml:space="preserve">et intra horam 211200 <lb/>menſurae, horis 24, menſurae 5, 068, 800, h. </s>
  <s xml:id="echoid-s550" xml:space="preserve">e. </s>
  <s xml:id="echoid-s551" xml:space="preserve">18102 <lb/>cadi uel modii aquae, facta diuiſione per 280. </s>
  <s xml:id="echoid-s552" xml:space="preserve">Et ſi <lb/>porro quaeratur, utrum haec aqua ab antliis ſuperiori-<lb/>bus hauriri et in aquaeductum protrudi queat, appa-<lb/>rebit, multo plus antlias ſuperiores attollere poſſe, ſi <lb/>omnes moueantur; </s>
  <s xml:id="echoid-s553" xml:space="preserve">quod tamen fierinequit, tum quia <lb/>flumen non ſemper tam uelociter in rotas irruit, tum <lb/>quia in tanta multitudine et longitudine catenarum et <lb/>antliarum, ſemper aliquae deficiunt, et reparatione <lb/>opus habent. </s>
  <s xml:id="echoid-s554" xml:space="preserve">Et quamuis aquise ſequana ductis etiam <lb/>fontium quaedam accedant, tamen quantitatem 18102 <lb/>cadorum, intra νυχθήμερον hauriendorum, quarta mi-<lb/>nimum parte multandam exiſtimem, ut medius nume-<lb/>rus obtineatur. </s>
  <s xml:id="echoid-s555" xml:space="preserve">Siquidem multum aquae perit in uia, <lb/>quae per anguſtas fiſtularum rimas penetrat, et frequen-<lb/>tius una alteraue machinae rota ſiſtenda eſt, pro emen-<lb/>dandis, quae quotidie ſeſe exſerunt, uitiis.</s>
  <s xml:id="echoid-s556" xml:space="preserve"/>
</p>
<pb o="26" file="0036" n="36" rhead="CAPVT I."/>
<p>
  <s xml:id="echoid-s557" xml:space="preserve">33. </s>
  <s xml:id="echoid-s558" xml:space="preserve">Difficillimum in tota hac contemplatione ca-<lb/>put eſt, quod ad tantae totque ex partibus conſtructae <lb/>machinae uires aeſtimandas ſpectat. </s>
  <s xml:id="echoid-s559" xml:space="preserve">Etſi enim ea uiui-<lb/>mus aetate, qua diligentia praeſtantiſſimorum ingenio-<lb/>rum, doctrina de corporum motionibus egregie elabo-<lb/>rata, multisque ueritatibus inſtructa eſt, quo nomine <lb/>prae ceteris laudem conſecuti ſunt Galileus, Toricel-<lb/>lius, Newtonus, Leibnitius, Bernoullii, Varignoni-<lb/>us, Hermannus, Graueſandius; </s>
  <s xml:id="echoid-s560" xml:space="preserve">neque defuerunt, <lb/>qui ſpeciatim fluminum curſus atque impetus perueſti-<lb/>garunt, et experientiam quoque ſtudioſe conſuluerunt, <lb/>quod Mariottium et Guilielminum feciſſe conſtat, ta-<lb/>men non diffitentur ipſi ſcrutatores reconditorum <lb/>eiusmodi naturae effectuum, uires quaeſitas plerum-<lb/>que magis ueriſimiliter innoteſcere, quam claris ex <lb/>principiis demonſtrari poſſe. </s>
  <s xml:id="echoid-s561" xml:space="preserve">Non uacat in praeſenti <lb/>latius excutere hoc argumentum, quamobrem ſufficiet <lb/>nobis, ſi euincere poſſimus, in magna illa, de qua lo-<lb/>quimur, machina, ſuperandis oneribus idoneam quo-<lb/>que et ſatis potentem reſpondere uirtutem.</s>
  <s xml:id="echoid-s562" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s563" xml:space="preserve">34. </s>
  <s xml:id="echoid-s564" xml:space="preserve">Ordo poſtulat, ut primum de mouendis ponde-<lb/>ribus ſoliciti ſimus. </s>
  <s xml:id="echoid-s565" xml:space="preserve">ſit exempli loco rota, quae altero <lb/>manubrio octo antlias prementes et unam aſpirantem <lb/>mouet, altero catenam trahit. </s>
  <s xml:id="echoid-s566" xml:space="preserve">Patuit ſupra, cylindros <lb/>aquae 64, diametri 6 digit. </s>
  <s xml:id="echoid-s567" xml:space="preserve">altos 4 pedes, pendere 3520 <lb/>libras, ex quo ſequitur, quod octo aequipolleant 440 <lb/>libris, additis 55 libris, quantum nempe una columna <lb/>grauitat, pro aſpirante, fient 495 librae. </s>
  <s xml:id="echoid-s568" xml:space="preserve">Non autem <lb/>ſolum hae aquae attolluntur, ſed propelluntur etiam a <lb/>fingulis 4 prementibus embolis, et per fiſtulas ad ca-<lb/>ſtellum medium aſſurgunt, et harum columnarum al-<lb/>titudo perpendicularis eſt 150 pedum. </s>
  <s xml:id="echoid-s569" xml:space="preserve">ſi diameter eadem <lb/>cum diametris antliarum, 6 digitorum, ponatur, con-
<pb o="27" file="0037" n="37" rhead="DE MACHINA MARLYENSI."/>
tinet talis columna columnas 37, altitudinis 4 pedum, <lb/>h. </s>
  <s xml:id="echoid-s570" xml:space="preserve">e. </s>
  <s xml:id="echoid-s571" xml:space="preserve">pondus 37. </s>
  <s xml:id="echoid-s572" xml:space="preserve">55 = 2035 librarum. </s>
  <s xml:id="echoid-s573" xml:space="preserve">duae habent 4070 <lb/>lib. </s>
  <s xml:id="echoid-s574" xml:space="preserve">additis 495 lib. </s>
  <s xml:id="echoid-s575" xml:space="preserve">oriuntur 4565. </s>
  <s xml:id="echoid-s576" xml:space="preserve">librae. </s>
  <s xml:id="echoid-s577" xml:space="preserve">hic numerus, pro <lb/>compenſando affrictu antliarum, uincendoque impe-<lb/>dimento, quod ab aquis poſt alas ſtagnantibus oritur, <lb/>ſumatur bis, et fient librae 9130. </s>
  <s xml:id="echoid-s578" xml:space="preserve">ſed quoniam onera <lb/>lignorum embolorumque, et ipſius rotae negleximus, <lb/>addantur denuo 2035 lib. </s>
  <s xml:id="echoid-s579" xml:space="preserve">ſumma 11165 propemodum in-<lb/>dicabit onus ab altero rotae manubrio ſuperandum.</s>
  <s xml:id="echoid-s580" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s581" xml:space="preserve">35. </s>
  <s xml:id="echoid-s582" xml:space="preserve">Quod attinet ad catenas, iſtae non minus nego-<lb/>tii rotis faceſſunt. </s>
  <s xml:id="echoid-s583" xml:space="preserve">Sumamus ordinem, qui in caſtello <lb/>ſiniſtro finitur, hic enim columnae aquarum fere ſimi-<lb/>les ſunt, undecim ex iis ualent 11. </s>
  <s xml:id="echoid-s584" xml:space="preserve">55 = 605 lib. </s>
  <s xml:id="echoid-s585" xml:space="preserve">et du-<lb/>plum ob affrictum et pondus embolorum 1210 lib. </s>
  <s xml:id="echoid-s586" xml:space="preserve">Por-<lb/>ro ex caſtello columnae duae aquae, intra fiſtulas, qua-<lb/>rum perpendicularis altitudo eſt 175 pedum, (§. </s>
  <s xml:id="echoid-s587" xml:space="preserve">26) <lb/>eleuantur. </s>
  <s xml:id="echoid-s588" xml:space="preserve">facta huius longitudinis diuiſione per 4, <lb/>continentur 44 columnae, 4 pedes longae, quare 44. <lb/></s>
  <s xml:id="echoid-s589" xml:space="preserve">55 = 2420 libris, et duplicato numero, pro columna <lb/>altera, 4840 lib. </s>
  <s xml:id="echoid-s590" xml:space="preserve">additaque priore ſumma 1210 lib. </s>
  <s xml:id="echoid-s591" xml:space="preserve">pro-<lb/>deunt 6050 librae. </s>
  <s xml:id="echoid-s592" xml:space="preserve">Cum autem aquis hiſce, intra fiſtu-<lb/>las propulſis, tum aeris pondus renitatur, tum inuer-<lb/>ſiones inflexionesque tuborum obſtacula obiiciant, ſe-<lb/>curius pro dato numero duplo maiorem 12100 aſſume-<lb/>mus, quo onus alterius manubrii ſignificetur, non ad-<lb/>modum diſſimile illius, quod oppoſito manubrio uin-<lb/>citur, ceterum ſumma totius molis uni rotae ſuperan-<lb/>dae et mouendae eſt 23265 librarum. </s>
  <s xml:id="echoid-s593" xml:space="preserve">Et pro rotis 14, <lb/>quia in ſingulas, ultima excepta, ſimilia fere onera <lb/>diſtributa ſunt, pondus mouendum fiet 325710 li-<lb/>brarum.</s>
  <s xml:id="echoid-s594" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s595" xml:space="preserve">36. </s>
  <s xml:id="echoid-s596" xml:space="preserve">Vtrum fluminis impetus tantae moli agitandae <lb/>par ſit, ſequenti modo indagabimus. </s>
  <s xml:id="echoid-s597" xml:space="preserve">ponamus rotas
<pb o="28" file="0038" n="38" rhead="CAPVT I."/>
ſingulas diametri 36 pedum alis praeditas 32, quae uni-<lb/>us pedis altitudinem, et quatuor pedum longitudinem <lb/>habent. </s>
  <s xml:id="echoid-s598" xml:space="preserve">Neque obeſt, quod nonnullis rotis altiores <lb/>alae imponantur, ſiquidem extra medium fluminis <lb/>curſum uerſus ripam remotae ſunt, ut maiorem aqua-<lb/>rum irruentium molem excipiant, et reliquarum con-<lb/>uerſionis celeritatem conſequantur, haec enim admini-<lb/>cula experientia reperta ſunt, quae tutiſſima aequatio-<lb/>nis eiusmodi inueniendae magiſtra eſſe poteſt. </s>
  <s xml:id="echoid-s599" xml:space="preserve">atque <lb/>ideo rotae in medio flumine ſuſpenſae nobis data quae-<lb/>dam, etiam reliquis, ſimili ui gaudentibus, applicanda <lb/>ſubminiſtrant. </s>
  <s xml:id="echoid-s600" xml:space="preserve">Porro ſequemur obſeruationes Ionche-<lb/>rii qui teſtatur p. </s>
  <s xml:id="echoid-s601" xml:space="preserve">158 (1) aquas fequanae aggere impedi-<lb/>tas, ſextuplo uelocius ruere, quam in alueo libero, <lb/>ſpeciatim prope Lutetiam Pariſiorum, e regione hoſpi-<lb/>tii inualidorum militum, et intra minutum ſecundum, <lb/>per lineam uiginti pedum prouolui, rotam uero intra <lb/>triginta ſecunda ſemel in orbem ire. </s>
  <s xml:id="echoid-s602" xml:space="preserve">(2) quod aqua ro-<lb/>tam pellens dimidio radii perpendicularis uel uertica-<lb/>lis immineat, eundemque tegat, adeoque ſex circiter <lb/>alas continuo impetu feriat.</s>
  <s xml:id="echoid-s603" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s604" xml:space="preserve">37. </s>
  <s xml:id="echoid-s605" xml:space="preserve">Praeterea huc repetendae ſunt leges ſecundum <lb/>quas aquae fluentes in alas rotarum obuias impetum <lb/>facere ſolent, de quibus earum diligens ſcrutator <emph style="sc">Ma-<lb/>riottius</emph> late exponit in tracta@@ de motu aquarum, <lb/>diſſertatione tertia, p. </s>
  <s xml:id="echoid-s606" xml:space="preserve">166. </s>
  <s xml:id="echoid-s607" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s608" xml:space="preserve">Pariſ. </s>
  <s xml:id="echoid-s609" xml:space="preserve">ſcilicet comparat <lb/>aquas per decliue fluentes, cum iis quae ex uaſe per <lb/>oſtium aliquod apertum proruunt, et cum deprehen-<lb/>deret, aquarum proſilientium celeritatem dependere <lb/>ab altitudine columnae aqueae aperto oſtio incumben-<lb/>tis, et a celeritate impetum, ſiue uim qua graue cor-<lb/>pus lapſu ſuo trudit, proficiſci, utriusque determina-<lb/>tionem, tum ex doctrinis de motu et lapſu grauium in
<pb o="29" file="0039" n="39" rhead="DE MACHINA MARLYENSI."/>
uniuerſum, tum ex obſeruationibus et experimentis, <lb/>inuenire ſtudet. </s>
  <s xml:id="echoid-s610" xml:space="preserve">Miſſis reliquis ad regulam duntaxat <lb/>quintam p. </s>
  <s xml:id="echoid-s611" xml:space="preserve">192. </s>
  <s xml:id="echoid-s612" xml:space="preserve">conuertor, quae ad praeſens omnino <lb/>ſpectat argumentum. </s>
  <s xml:id="echoid-s613" xml:space="preserve">Docet ibidem, quod iactus <lb/>aquae eadem uelocitate, ſed per diuerſa oſtia ſalientis, <lb/>impetu ſuo aequilibres ſint ponderibus, quae habent <lb/>rationem duplicatam diametrorum foraminum, per <lb/>quae aqua emittitur. </s>
  <s xml:id="echoid-s614" xml:space="preserve">Cum enim antea demonſtraſſet, <lb/>aquas pondus obuium lapſu mouere poſſe, et lapſum <lb/>tanto fortiorem eſſe, quanto maior eſt aquae irruentis <lb/>copia, exinde regula illa ſequebatur, quia ſi oſtia cir-<lb/>culi figura fuerint praedita, eadem ſeruant rationem <lb/>duplicatam ſemidiametrorum, et tum uelocitas uel-<lb/>uti altitudinem cylindrorum aqueorum definit, hac <lb/>eadem exiſtente, res redibat ad materiam, cuius in <lb/>ſimilibus corporibus eadem eſt quae baſium ratio, al-<lb/>titudine non mutata. </s>
  <s xml:id="echoid-s615" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s616" xml:space="preserve">198. </s>
  <s xml:id="echoid-s617" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s618" xml:space="preserve">Idemque expe-<lb/>rientia comprobauit. </s>
  <s xml:id="echoid-s619" xml:space="preserve">Nam ad axem uolubilem aptauit <lb/>alam aliquam, quae pondus adducebat, et ſuſpenſa ea-<lb/>dem intra aquam fluentem, cuius antea celeritatem <lb/>alio modo repererat, notauit eandem proportionem <lb/>ponderis et impetus, quae auxilio tubi, ex quo aqua <lb/>ſaliens obuium aliquod corpus impellit et ſuſtentat, <lb/>fuerat inuenta. </s>
  <s xml:id="echoid-s620" xml:space="preserve">Videlicet aqua celeritate 3 pedum in-<lb/>tra minutum ſecundum ruens, tantundem hoc motu <lb/>praeſtat, quantum alia, quae ex cylindro 12 pedes alto <lb/>delabitur. </s>
  <s xml:id="echoid-s621" xml:space="preserve">aequipollet autem impetus eiusdem, ſi alae <lb/>baſis fuerit quadrata, cuius latus dimidium pedem ca-<lb/>pit, 210 libris, multiplicata nempe baſi quadrata in al-<lb/>titudinem, quo facto producitur priſma trium pedum <lb/>cubicorum, et quoniam quilibet pes cubicus aquae ua-<lb/>let 70 libras vid. </s>
  <s xml:id="echoid-s622" xml:space="preserve">p. </s>
  <s xml:id="echoid-s623" xml:space="preserve">192. </s>
  <s xml:id="echoid-s624" xml:space="preserve">tres pedes dabunt 210 libras. <lb/></s>
  <s xml:id="echoid-s625" xml:space="preserve">Celeritatem autem aquae per perpendiculum 12 pedum
<pb o="30" file="0040" n="40" rhead="CAPVT I."/>
labentis, ſecundum Galileum aeſtimat 24 pedum in-<lb/>tra minutum ſecundum. </s>
  <s xml:id="echoid-s626" xml:space="preserve">Itaque per hanc hypothe-<lb/>ſin, aqua cuius celeritas eſt 24 ped. </s>
  <s xml:id="echoid-s627" xml:space="preserve">intra minutum ſe-<lb/>cundum impellens alam {1/2} p. </s>
  <s xml:id="echoid-s628" xml:space="preserve">□. </s>
  <s xml:id="echoid-s629" xml:space="preserve">aequiualet 210 libris. <lb/></s>
  <s xml:id="echoid-s630" xml:space="preserve">Poſita autem celeritate fluminis aggere impediti 20 <lb/>pedum, apparet, hanc habere prioris celeritatis {5/6}, cu-<lb/>ius quadratum eſt {25/36}, quod ex 210 libris dabit 145 li-<lb/>bras, quae imminent alae, cuius latus dimidio pedi <lb/>aequale exiſtit. </s>
  <s xml:id="echoid-s631" xml:space="preserve">itaque ſuper pede integro quadratum <lb/>pondus 580 lib. </s>
  <s xml:id="echoid-s632" xml:space="preserve">et ſuper ala 1 p. </s>
  <s xml:id="echoid-s633" xml:space="preserve">alta 4 p. </s>
  <s xml:id="echoid-s634" xml:space="preserve">longa iterum <lb/>quatuor tales columnae, nempe 2320 librae, conſiſtunt. </s>
  <s xml:id="echoid-s635" xml:space="preserve"><lb/>Haec eſt illa uis motrix, quae alicui alae rotae Marly-<lb/>enſis in medio flumine poſitae incumbit. </s>
  <s xml:id="echoid-s636" xml:space="preserve">Enimuero <lb/>non unam alam tantum pondus pellit, quia ſex alae ſi-<lb/>mulut plurimum feriuntur. </s>
  <s xml:id="echoid-s637" xml:space="preserve">Non omnes tamen recta <lb/>urget talis tantaque uirtus; </s>
  <s xml:id="echoid-s638" xml:space="preserve">ſoli radio uerticali oc-<lb/>currit, in obliquis minor eſt, quia uis creſcit uel decre-<lb/>ſcit pro ratione diſtantiae puncti applicationis ab hy-<lb/>pomochlio, (§. </s>
  <s xml:id="echoid-s639" xml:space="preserve">30. </s>
  <s xml:id="echoid-s640" xml:space="preserve">Inſtit. </s>
  <s xml:id="echoid-s641" xml:space="preserve">mechan.) </s>
  <s xml:id="echoid-s642" xml:space="preserve">quadrante igitur <lb/>rotae, cuius radius 18 p. </s>
  <s xml:id="echoid-s643" xml:space="preserve">in octo partes aequales diui-<lb/>ſo, radii ad puncta diuiſionis educti intercipient ſinguli <lb/>cum uicino angulum 11 gr. </s>
  <s xml:id="echoid-s644" xml:space="preserve">15. </s>
  <s xml:id="echoid-s645" xml:space="preserve">min. </s>
  <s xml:id="echoid-s646" xml:space="preserve">qualis eſt, quem com-<lb/>prehendit radius primus obliquus cum uerticali, ſe-<lb/>cundus cum eodem uerticali faciet angulum 22 gr. </s>
  <s xml:id="echoid-s647" xml:space="preserve">30 <lb/>m. </s>
  <s xml:id="echoid-s648" xml:space="preserve">tertius cum uerticali angulum conſtituet 33 gr. </s>
  <s xml:id="echoid-s649" xml:space="preserve">45 <lb/>quartus 45. </s>
  <s xml:id="echoid-s650" xml:space="preserve">quintus 56 gr. </s>
  <s xml:id="echoid-s651" xml:space="preserve">15 m. </s>
  <s xml:id="echoid-s652" xml:space="preserve">diſtantiae autem re-<lb/>ctae ab hypomochlio, ſiue a centro rotae, reſpondent <lb/>ſinibus complementi angulorum, quos modo comme-<lb/>moraui. </s>
  <s xml:id="echoid-s653" xml:space="preserve">ex quo apparet, in radiis obliquis quinque uir-<lb/>tutem 2320. </s>
  <s xml:id="echoid-s654" xml:space="preserve">libr. </s>
  <s xml:id="echoid-s655" xml:space="preserve">decreſcere pro ratione ſinuum com-<lb/>plementi laudatorum angulorum; </s>
  <s xml:id="echoid-s656" xml:space="preserve">dataque ratione ſi-<lb/>nus totius et ſinuum complementi, decrementa uirium <lb/>rationibus rite ſubductis innoteſcent. </s>
  <s xml:id="echoid-s657" xml:space="preserve">ſequens tabula
<pb o="31" file="0041" n="41" rhead="DE MACHINA MARLYENSI."/>
exhibet rationem ſinus totius et ſinuum complementi, <lb/>cum debita quantitate uirium radiis obliquis immi-<lb/>nentium.</s>
  <s xml:id="echoid-s658" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve"> <lb/>anguli \\ radior rotae # Sin. tor. # S. compl. # Impetus aquae <lb/>0 # 0 # 0 # 2320 librar. <lb/>0 1 <lb/>11. 15. # 1000 # 980 # 2273 <lb/>22. 30. # 1000 # 923 # 2141 <lb/>33. 45. # 1000 # 831 # 1928 <lb/>45. 0. # 1000 # 707 # 1640 <lb/>56. 15. # 1000 # 555 # 1287 <lb/></note>
<p>
  <s xml:id="echoid-s659" xml:space="preserve">His uiribus in ſummam collectis, prodeunt 11592 librae, <lb/>quae in peripheria rotae applicatae eandem onere ſuo <lb/>propellunt. </s>
  <s xml:id="echoid-s660" xml:space="preserve">Quoniam autem rotae axi inſertum eſt <lb/>manubrium curuatum, quo libramenta embolos uel <lb/>catenas trahentia agitantur, cuius longitudinem ſupra <lb/>§. </s>
  <s xml:id="echoid-s661" xml:space="preserve">13 indicauimus trium pedum, uelpotius 2 {1/2}, ſpiſſitu-<lb/>dine metalli utrique extremo demta, reſtat, ut quanta <lb/>uis in manubriis occurrat, definiamus. </s>
  <s xml:id="echoid-s662" xml:space="preserve">Notum hic <lb/>aſſumo ex mechanicae diſciplinae elementis, in axe <lb/>cum peritrochio rationem’ uirium in peripheria adhi-<lb/>bitarum, ad pondus ſuper axe motum, reciproce eſſe <lb/>talem, qualis inter ſemidiametrum axis et ſemidiame-<lb/>trum rotae intercedit, (§. </s>
  <s xml:id="echoid-s663" xml:space="preserve">38. </s>
  <s xml:id="echoid-s664" xml:space="preserve">Inſtit. </s>
  <s xml:id="echoid-s665" xml:space="preserve">Mechan.) </s>
  <s xml:id="echoid-s666" xml:space="preserve">eſt enim <lb/>in rotis Marlyenſibus manubrium, quod onus ducit, lo-<lb/>co medii axis, quamobrem uti longitudo manubrii ha-<lb/>bet ſe ad ſemidiametrum rotae, ita uis huius periphe-<lb/>riae inſidens, ad pondus mouendum aequilibre, et quia <lb/>non ſolum in extremo radii uerum in aliis quinque <lb/>obliquis uis a pondere et impetu aquarum oriunda ſe-
<pb o="32" file="0042" n="42" rhead="CAPVT I."/>
ſe exſerit, neceſſum eſt, ut ſingulas illas radiorum obli-<lb/>quorum diſtantias rectas a centro, quas antea ſinus <lb/>complementi laudatorum angulorum nominauimus, <lb/>cum longitudine manubrii comparemus, et ope re-<lb/>ſpondentis iisdem uirtutis, eam particulam uirium <lb/>quaeramus, quae manubrii extremo debetur, tum <lb/>enim additis iſtis uiribus, cognoſcitur integra uirtus, <lb/>qua manubrium adducitur. </s>
  <s xml:id="echoid-s667" xml:space="preserve">Calculus manifeſtat nu-<lb/>meros ſequentes,</s>
</p>
<note position="right" xml:space="preserve"> <lb/>1. pro radio uerticali, # 16704 <lb/>2. pro primo obliquo, # 15911 <lb/>3. pro ſecundo obliquo, # 14045 <lb/>4. pro tertio obl. # 11332 <lb/>5. pro quarto obl. # 8331 <lb/>6. pro quinto obliquo. # 5148 <lb/># 71471 <lb/></note>
<p>
  <s xml:id="echoid-s668" xml:space="preserve">Itaque una rota in machina Marlyenſi impellitur ui <lb/>71471 librarum, et pro rotis 14 reperiuntur 1000594 li-<lb/>brae. </s>
  <s xml:id="echoid-s669" xml:space="preserve">Ceterum conſultum duxi, paulo diſtinctius de-<lb/>ſcribere calculi illius leges, et ſingulos quoque nume-<lb/>ros repertos afferre, tum quia hoc exemplum ad aeſti-<lb/>mationem uirium in machinis ſimilibus uſum praebere <lb/>poteſt, tum etiam, ut de diſſeniu, qui hic inter Ion-<lb/>cherii et meas rationes occurrit, iudicium a lectore <lb/>ferri, uel examen utriusque aſſertionis facilius inſtitui <lb/>poſſit. </s>
  <s xml:id="echoid-s670" xml:space="preserve">Tametſi enim mihi conſtet ex aliis indiciis, <lb/>Dn. </s>
  <s xml:id="echoid-s671" xml:space="preserve">Ioncherium eadem Mariottii experimenta, quibus <lb/>etiam meus calculus nititur, ſequi, uid. </s>
  <s xml:id="echoid-s672" xml:space="preserve">173. </s>
  <s xml:id="echoid-s673" xml:space="preserve">tamen <lb/>tacet ille omnino regulas, quibus numeros ſuos ac-<lb/>commodauit, nec Mariottii meminit, nec modum pro-
<pb o="33" file="0043" n="43" rhead="DE MACHINA MARLYENSI."/>
poſitum problem a fo luendi manifeſtat. </s>
  <s xml:id="echoid-s674" xml:space="preserve">Proferam ipſa <lb/>eiusdem uerba, quae huc pertinent. </s>
  <s xml:id="echoid-s675" xml:space="preserve">poſtquam enim <lb/>de magnitudine rotae et alarum, et manubrii, nec non <lb/>de celeritate aquarum, et numero alarum, quas impel-<lb/>lunt, dixiſſet, ita tandem concludit p. </s>
  <s xml:id="echoid-s676" xml:space="preserve">158. </s>
  <s xml:id="echoid-s677" xml:space="preserve">La hauteur <lb/>de l’eau couvroit la moitie du rayon perpendiculaire, et les <lb/>6 aubes continuellement frapées dans ce cas, mais frapées <lb/>obacune en particulier, ſelon la diverſité de leurs angles, <lb/>imprimoient toutes enſemble à l’ extremité de la manivelle <lb/>la force de 81467 liv. </s>
  <s xml:id="echoid-s678" xml:space="preserve">trente ſept ſoixantiemes. </s>
  <s xml:id="echoid-s679" xml:space="preserve">Pour faire <lb/>cette regle, il faut d’ abord calculer les 4 pieds quarrés d’ <lb/>aubes, par la viteſſe de 20 pieds par ſeconde, comme ſi’ils <lb/>en etoient frapés perpendiculairement, puis imaginant un <lb/>rayon horizontal, on dira, comme le rayon elevé ſur le rayon <lb/>horizontal, ainſi la ſomme dont les quatre pieds d’aubes ſont <lb/>frapez ſuivant leurs degrez d’elevation. </s>
  <s xml:id="echoid-s680" xml:space="preserve">et pour ſavoir la for <lb/>ce, avec laquelle ce poids fait agir la manivelle, il faudra <lb/>faire cette proportion reciproque, comme la longeur de la <lb/>manivelle eſt à la partie du rayon compriſe entre le centre <lb/>de la roue, et le centre de la palette touchée par l’eau, ainſi <lb/>la force dont les 4 pieds d’aubes ſont frapez ſuivant leurs <lb/>ſinus, eſt a la force, qui eſt imprimée a l’ extremité de la <lb/>manivelle, faiſant ces deux analogies pour toutes les 6 aubes <lb/>ſeparement, et additionant ces differentes ſommes, on aura <lb/>la valeur de 81467 tren ſept ſoixantiemes. </s>
  <s xml:id="echoid-s681" xml:space="preserve">Vndetantum <lb/>inter ſe differant rationes nondum mihi patet. </s>
  <s xml:id="echoid-s682" xml:space="preserve">meas <lb/>enim diligenter iterum excuſſi, et eas rite ſe habere <lb/>deprehendi. </s>
  <s xml:id="echoid-s683" xml:space="preserve">Poteſt tamen in proportionibus manu-<lb/>brii ad radium et ſinus complementi laudatos diſcri-<lb/>men deliteſcere; </s>
  <s xml:id="echoid-s684" xml:space="preserve">ſiquidem prolixus eſt ille calculus, <lb/>ubi leuis differentia ſub initium admiſſa, et per plures <lb/>numeros continuata maiorem diſſenſum parere non <lb/>difficulter poteſt. </s>
  <s xml:id="echoid-s685" xml:space="preserve">Forſitan etiam in primo numero
<pb o="34" file="0044" n="44" rhead="CAPVT I."/>
tantum uitium latet, qui<unsure/>a reliqui ſatis apte conſen-<lb/>tiunt.</s>
  <s xml:id="echoid-s686" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s687" xml:space="preserve">38. </s>
  <s xml:id="echoid-s688" xml:space="preserve">Peropportune interim accidit, ut magnus ita ex-<lb/>ceſſus uirium, ſi ponderum mouendorum ratio habea-<lb/>tur, in machina Marlyenſi occurrat. </s>
  <s xml:id="echoid-s689" xml:space="preserve">Nam non ſem-<lb/>per ea, quam aſſumſimus fluminis altitudo eſt, nec <lb/>aquae per totum uolumen ſuum ſimilem ubique per-<lb/>cuſſionem efficiunt, ſiquidem diligentior huius materiae <lb/>perueſtigatio oſtendit, aquas in alueo ſuo deuolutas <lb/>non omnes eandem aſſequi uelocitatem quia ſuperio-<lb/>res, etſi cum inferioribus ſecundum eandem decliuita-<lb/>tem progrediantur, liberius tamen his mouentur, quae <lb/>et plus ab incumbentibus onerantur, et propria tenaci-<lb/>tate retinentur. </s>
  <s xml:id="echoid-s690" xml:space="preserve">Agit de hac re ex inſtituto <emph style="sc">Mariot</emph>-<lb/><emph style="sc">TIVS</emph> Part. </s>
  <s xml:id="echoid-s691" xml:space="preserve">2. </s>
  <s xml:id="echoid-s692" xml:space="preserve">p. </s>
  <s xml:id="echoid-s693" xml:space="preserve">200 ſq. </s>
  <s xml:id="echoid-s694" xml:space="preserve">et inprimis experimenta quae-<lb/>dam laudat, quae hic eiusdem uerbis repeti merentur. <lb/></s>
  <s xml:id="echoid-s695" xml:space="preserve">J ay encore remarque ſouvent des herbes, que l’eau emme-<lb/>noit, et je voyo<unsure/>is manifeſtement, que celles qui etant entre <lb/>deux eaux pres du fond plus avancées, que celles qui etoient pres <lb/>de la ſurface, etoient bientot paſſées et laiſſées en arriere par les <lb/>ſuperieures; </s>
  <s xml:id="echoid-s696" xml:space="preserve">et ſi je jettois dans le meme courant une poignée <lb/>de groſſes ſcieures de bois qui alloient au fond plutot les unes <lb/>que les autres, je voyois toujours les ſuperieures preceder les <lb/>autres par ordre à proportion, qu’elles etoient plus ou moins <lb/>eloignées du fond. </s>
  <s xml:id="echoid-s697" xml:space="preserve">des quelles experie@ces il paroit, que dans <lb/>les rivieres qui coulent librement, l’eau ſuperieure va plus <lb/>vite que celle qui eſt proche du fond, et que dans celles qui <lb/>ſont contraintes de paſſer en un lieu etroit, etant retenuës <lb/>de deux cotés, celle du milieu va plus vite, que celle de la <lb/>ſurface, s’il n’y a que trois ou quatre pieds de profondeur. </s>
  <s xml:id="echoid-s698" xml:space="preserve"><lb/>add. </s>
  <s xml:id="echoid-s699" xml:space="preserve"><emph style="sc">Dechales</emph> Mund. </s>
  <s xml:id="echoid-s700" xml:space="preserve">Math. </s>
  <s xml:id="echoid-s701" xml:space="preserve">Tom. </s>
  <s xml:id="echoid-s702" xml:space="preserve">3. </s>
  <s xml:id="echoid-s703" xml:space="preserve">p. </s>
  <s xml:id="echoid-s704" xml:space="preserve">138.</s>
  <s xml:id="echoid-s705" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s706" xml:space="preserve">39. </s>
  <s xml:id="echoid-s707" xml:space="preserve">Quae autem antea § 34. </s>
  <s xml:id="echoid-s708" xml:space="preserve">et 38. </s>
  <s xml:id="echoid-s709" xml:space="preserve">dixi, de augen-<lb/>da quantitate ponderis mouendi ob affrictum et aquas
<pb o="35" file="0045" n="45" rhead="DE MACHINA MARLYENSI."/>
poſt alas parumper ſtagnantes, et noua ui propellen-<lb/>das, iterum iuuauerit illuſtrare iudicio conſenſuque in-<lb/>dagatoris huius argumenti ſolertiſſimi, Mariottii, qui <lb/>diu regis ſtipendiis eum ipſum in finem gauiſus eſt, ut <lb/>fluidorum motus obſeruationibus ſuis manifeſtius cer-<lb/>tiusque demonſtraret, quemadmodum ipſius in expe-<lb/>rimentis capiendis olim ſocius ingenioſiſſimus P. </s>
  <s xml:id="echoid-s710" xml:space="preserve"><emph style="sc">Se</emph>-<lb/><emph style="sc">BASTIANVS</emph> <emph style="sc">Trvchetvs</emph>, mihi ſaepius confirma-<lb/>uit. </s>
  <s xml:id="echoid-s711" xml:space="preserve">Explicaturus igitur Mariotius molarum ſupra ſe-<lb/>quanae flumine funibus ad ripas utrimque extenſis af-<lb/>fixarum nec non machinae hydraulicae, quae Samari-<lb/>tana uocatur, conditionem, docet, dimidium uirium <lb/>ob affrictum partium et ob aquas ſtagnantes interire. <lb/></s>
  <s xml:id="echoid-s712" xml:space="preserve">Ita enim ſcribit Tr. </s>
  <s xml:id="echoid-s713" xml:space="preserve">laudato Part. </s>
  <s xml:id="echoid-s714" xml:space="preserve">2. </s>
  <s xml:id="echoid-s715" xml:space="preserve">p. </s>
  <s xml:id="echoid-s716" xml:space="preserve">197. </s>
  <s xml:id="echoid-s717" xml:space="preserve">Les rouës <lb/>des moulins, qui ſont ſur la ſeine a Paris, entre le pont neuf <lb/>et le pont au change, n’ont à leurs extremités que la moi-<lb/>tié de la viteſſe de l’eau courante qui les choque, ce qui re-<lb/>vient à là même choſe, que lorsqu’ un poids en mouvement en <lb/>rencontre un autre immobile de même peſanteur, et qu’il ſ’y <lb/>attache, car etant joints enſemble, ils n’ont incontinent apr es <lb/>le choc, que la moitié de la viteſſe de celui qui a choqué, et <lb/>ainſi on peut ſuppoſer, que la reſiſtance du frotement de l’eſſi-<lb/>eu de la rouë, de celui de la meule, et du grain qu’elle briſe, <lb/>joint au poids de la rouë et de ſes pallettes, vaut autant à peu <lb/>prés que la reſiſtance@d’ un poids egal à celuy de l’ eau qui <lb/>choque, et par conſequent elles doivent retarder de moitie à <lb/>peu pres la viteſſe de l’eau qui les choque; </s>
  <s xml:id="echoid-s718" xml:space="preserve">on remarqne la <lb/>même proportion dans la rouë de la pompe de la Samaritaine. </s>
  <s xml:id="echoid-s719" xml:space="preserve"><lb/>Quod ſpeciatim attinet ad affrictum, qui in machina <lb/>Marlyenſi multiplex admodum in axibus rotarum cru-<lb/>cium, libramentorum, catenarum, et qui praecipue at-<lb/>tendi meretur, antliarum, occurrit, de eo quoque hic <lb/>nonnihil latius agere operae pretium uidetur. </s>
  <s xml:id="echoid-s720" xml:space="preserve">Eſt au-
<pb o="36" file="0046" n="46" rhead="CAPVT I."/>
tem affrictus conſideratio difficilior quam quis credide-<lb/>rit. </s>
  <s xml:id="echoid-s721" xml:space="preserve">Scilicet quaeritur de obſtaculis, quae naſcuntur, dum <lb/>corpus toto ſuo pondere ſuper altero nitens, eidemque <lb/>incumbens, ſuper eodem eſt mouendum. </s>
  <s xml:id="echoid-s722" xml:space="preserve">Hic remo-<lb/>ram primo ponit inaequalitas ſuperficierum corporum <lb/>ſeſe tangentium, miſcentur caua prominentibus ſolidis <lb/>partibus, totidem ueluti interueniunt elateria, quot <lb/>eminent monticuli, et dum ſingula renituntur, ſingula <lb/>augentmotus difficultatem. </s>
  <s xml:id="echoid-s723" xml:space="preserve">ex quo ſequitur, corpora, <lb/>quo inaequalia magis et aſpera item quo molliora ſun@, <lb/>eo plura in iis impedimenta motuum deprehendi. </s>
  <s xml:id="echoid-s724" xml:space="preserve">Et <lb/>quoniam elateria modo laudata, tanto fortius obſiſt<unsure/>unt, <lb/>quanto magis curuantur, apparet, prae ceteris ad am-<lb/>plificandam affrictus difficultatem multum conferre mo-<lb/>lis alteri inſidentis pondus, et dum ob priorem cauſam, <lb/>nempe aſperitatem, motus impedimenta creſcunt pro <lb/>ratione amplitudinis ſuperficiei, ob grauitatem denuo <lb/>et experientia teſte, multo maius augmentum conſe-<lb/>quuntur, quod potiſſimum <emph style="sc">Hirei</emph> et <emph style="sc">Amontonii</emph> phi-<lb/>loſophorum celeberrimorum opera diligentiaque eſt <lb/>demonſtratum. </s>
  <s xml:id="echoid-s725" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s726" xml:space="preserve">D<emph style="sc">N. DE</emph> <emph style="sc">Fontenelle</emph> Hiſt. </s>
  <s xml:id="echoid-s727" xml:space="preserve">Acad. <lb/></s>
  <s xml:id="echoid-s728" xml:space="preserve">R. </s>
  <s xml:id="echoid-s729" xml:space="preserve">ſc. </s>
  <s xml:id="echoid-s730" xml:space="preserve">a. </s>
  <s xml:id="echoid-s731" xml:space="preserve">1699. </s>
  <s xml:id="echoid-s732" xml:space="preserve">p. </s>
  <s xml:id="echoid-s733" xml:space="preserve">128. </s>
  <s xml:id="echoid-s734" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s735" xml:space="preserve">Etſi quis exiſtimet, tolli omni-<lb/>no primam cauſam poſſe, ſi polities inducatur corpori-<lb/>bus, et materia pingui u. </s>
  <s xml:id="echoid-s736" xml:space="preserve">g. </s>
  <s xml:id="echoid-s737" xml:space="preserve">oleo amplius lubricetur, <lb/>fallitur omnino. </s>
  <s xml:id="echoid-s738" xml:space="preserve">Siquidem pol@@ies et pinguedo ex-<lb/>cludunt aerem, qui caua inter corpora reſidua replet, <lb/>quo facto aer exterior incumbens tota ſua grauitate, <lb/>nouum et ualidiſſimum motui obſtaculum producit, <lb/>uti marmorum laeuigatorum ſibique impoſitorum ex-<lb/>perimentis conſtat. </s>
  <s xml:id="echoid-s739" xml:space="preserve">Et quis ignorat, quae hodie de <lb/>mutua corporum attractione, tanquam aeterna natu-<lb/>rae lege, philoſophi tradunt, quae utrum in ſingula-<lb/>ribus coniungendis, affrictuque eorum augendo, mo-
<pb o="37" file="0047" n="47" rhead="DE MACHINA MARLYENSI."/>
mentum habere queat, explorandum reſtat. </s>
  <s xml:id="echoid-s740" xml:space="preserve">conf. </s>
  <s xml:id="echoid-s741" xml:space="preserve"><emph style="sc">Dn</emph>. <lb/></s>
  <s xml:id="echoid-s742" xml:space="preserve"><emph style="sc">Gravesande</emph> Inſtit. </s>
  <s xml:id="echoid-s743" xml:space="preserve">Philoſ. </s>
  <s xml:id="echoid-s744" xml:space="preserve">Nevvton. </s>
  <s xml:id="echoid-s745" xml:space="preserve">p. </s>
  <s xml:id="echoid-s746" xml:space="preserve">u. </s>
  <s xml:id="echoid-s747" xml:space="preserve">et 333. </s>
  <s xml:id="echoid-s748" xml:space="preserve">Ex <lb/>his intelligi poteſt, quid requiratur ad iudicium de af-<lb/>frictu machinarum ferendum. </s>
  <s xml:id="echoid-s749" xml:space="preserve">Glaciem laudabili in-<lb/>ſtituto fregit <emph style="sc">Amontonivs</emph>, in commentariis acad. </s>
  <s xml:id="echoid-s750" xml:space="preserve"><lb/>reg. </s>
  <s xml:id="echoid-s751" xml:space="preserve">ſcientiarum, a. </s>
  <s xml:id="echoid-s752" xml:space="preserve">1699. </s>
  <s xml:id="echoid-s753" xml:space="preserve">p. </s>
  <s xml:id="echoid-s754" xml:space="preserve">257. </s>
  <s xml:id="echoid-s755" xml:space="preserve">edit. </s>
  <s xml:id="echoid-s756" xml:space="preserve">Amſtel. </s>
  <s xml:id="echoid-s757" xml:space="preserve">reperitque <lb/>experientiae conueniens, quod in materia, ex qua prae-<lb/>cipue machinae componuntur, ligno, ferro, cupro, <lb/>plumbo et ſimilibus, reniſus oriatur ab affrictu talis, qui <lb/>tertiae parti ponderis, quod ſubiectum corpus premit, <lb/>reſpondeat. </s>
  <s xml:id="echoid-s758" xml:space="preserve">Haec ſi transferantur ad machinam Mar-<lb/>lyenſem, nemo uitio mihi uertet, quod dimidia parte <lb/>uires machinae affrictu minui dixerim. </s>
  <s xml:id="echoid-s759" xml:space="preserve">Non ſolum <lb/>enim ibi magnum occurrit pondus rotarum libramen-<lb/>torum embolorumque, ſed etiam in his poſtremis, <lb/>dum lignum molle et corium humidum in antliis agi-<lb/>tatur, ita attritus uidetur exaſperari, ut aeſtimationem <lb/>adhuc maiorem, quam aſſumſi requirat. </s>
  <s xml:id="echoid-s760" xml:space="preserve">Siquidem et-<lb/>iam pondus aereae columnae imminentis embolo, ſub <lb/>quo aer craſſus excluſus eſt, ſuperandum uenit. </s>
  <s xml:id="echoid-s761" xml:space="preserve">tandem <lb/>accedit his inertia aquarum poſt alas ſtagnantium, cui <lb/>ſoli maximam uim tribuit Mariottius. </s>
  <s xml:id="echoid-s762" xml:space="preserve">Praeterea res <lb/>ipſa loquitur, hypotheſin meam admittendam eſſe. </s>
  <s xml:id="echoid-s763" xml:space="preserve"><lb/>nam aucto ad dimidium onere, tamen uis ſupereſt agi-<lb/>tandae machinae, e@ praeſtandis iis quorum cauſa in-<lb/>uenta et exſtructa eſt. </s>
  <s xml:id="echoid-s764" xml:space="preserve">in ipſis autem uiribus nullum ex-<lb/>ceſſum commiſſum eſſe, ſi ea, quae aliorum obſeruatio-<lb/>nibus fidem habens attuli, uera ſint, palam eſſe arbi-<lb/>tror. </s>
  <s xml:id="echoid-s765" xml:space="preserve">Rectiſſime etiam ſentiunt, qui ſuadent, tutius <lb/>eſſe in pragmatia machinali, obſtaculorum nondum re-<lb/>cte cognitorum momenta auctiora ſumere, quam his <lb/>extenuatis, nimis confidere inuentae compoſitionis ali-<lb/>cuius machinae facultatibus. </s>
  <s xml:id="echoid-s766" xml:space="preserve">Et placet mihi prae reli-
<pb o="38" file="0048" n="48" rhead="CAP. I. DE MACHINA MARLYENSI."/>
quis iudicium accuratum uiri laude mea maioris <emph style="sc">Dn</emph>. <lb/></s>
  <s xml:id="echoid-s767" xml:space="preserve"><emph style="sc">Fontenellii</emph> l. </s>
  <s xml:id="echoid-s768" xml:space="preserve">c. </s>
  <s xml:id="echoid-s769" xml:space="preserve">p. </s>
  <s xml:id="echoid-s770" xml:space="preserve">134. </s>
  <s xml:id="echoid-s771" xml:space="preserve">Cet effet du frottement ſeul <lb/>peut paroitre etonnant, et fort au deſſus de ce qu’on en au-<lb/>roit imaginé à vuë de paîs. </s>
  <s xml:id="echoid-s772" xml:space="preserve">par la il eſt aiſé de voir, combien <lb/>l’ on doit ſe meprendre, dans le calcul d’une machine, quand <lb/>on n’y conſidere que les rapports de la puiſſance et du poids, <lb/>et de leur diſtance du point d’ appui, et que l’on neglige les <lb/>frottement, comme on fait d’ ordinaire, ou du moins, que <lb/>l’ on compte qu’ils n’iront pas bien haut. </s>
  <s xml:id="echoid-s773" xml:space="preserve">Il ſe peut faire <lb/>aiſement, que la puiſſance perde par le frottement tout l’a-<lb/>vantage, qu’elle aura menagée, et que même elle devienne <lb/>malgré cela fort inferieure au poids.</s>
  <s xml:id="echoid-s774" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s775" xml:space="preserve">40. </s>
  <s xml:id="echoid-s776" xml:space="preserve">Sub finem huius capitis addam monitum ge-<lb/>nerale, ad totius machinae Marlyacenſis conformatio-<lb/>nem pertinens. </s>
  <s xml:id="echoid-s777" xml:space="preserve">Conſtat inſignem uim eſſe caloris et <lb/>frigoris, in expandenda et contrahenda qualibet mate-<lb/>ria. </s>
  <s xml:id="echoid-s778" xml:space="preserve">Cum itaque in regio illo, de quo hactenus expli-<lb/>cui, opere, tanta multitudo, tantaque porrectio longu-<lb/>riorum ferreorum in catenis et antliarum apparatu ex-<lb/>iſtat, experientia docuit, ferra haec praelonga frigore <lb/>contracta, aum arctius connexa id liberius facere non <lb/>poſſent, rupta ſaepenumero fuiſſe, et alio tempore ca-<lb/>lore expanſa, difficilem machinae motum reddidiſſe. <lb/></s>
  <s xml:id="echoid-s779" xml:space="preserve">Vtrique uitio tandem medela adhibita eſt, laxiore fer-<lb/>rorum copulatione facta, claui@@empe gracilioribus in <lb/>ampliora foramina immiſſis, embolisque et aliis mem-<lb/>bris ſimiliter ſuſpenſis, ut omnem in caſum aliqua eo-<lb/>rum uacillatio relinqueretur.</s>
  <s xml:id="echoid-s780" xml:space="preserve"/>
</p>
<pb o="39" file="0049" n="49"/>
</div>
<div xml:id="echoid-div13" type="section" level="1" n="9">
<head xml:id="echoid-head20" xml:space="preserve">CAPVT II. <lb/>DE <lb/>MACHINIS HYDRAVLICIS <lb/>QVIBVS PARISIIS AQVAE <lb/>EX SEQVANA FLVVIO <lb/>HAVRIVNTVR</head>
<head xml:id="echoid-head21" xml:space="preserve">1.</head>
<p>
  <s xml:id="echoid-s781" xml:space="preserve">Iuxta pontem B. </s>
  <s xml:id="echoid-s782" xml:space="preserve">Virginis ſequenti machina, a Ran-<lb/>nequinio filio, qui etiam hodie illi praefectus eſt, <lb/>inuenta, aquae in altum tolluntur. </s>
  <s xml:id="echoid-s783" xml:space="preserve">Poſt pontem me-<lb/>dium ſuper palis contignationes aliquot quieſcunt. <lb/></s>
  <s xml:id="echoid-s784" xml:space="preserve">imo loco e regione duorum arcuum, ſuſpenſae ſunt ro-<lb/>tae duae, quarum diameter eſt 28 pedum, et in inter-<lb/>na rotarum peripheria aſſeres, tanquam alae 18 p. </s>
  <s xml:id="echoid-s785" xml:space="preserve">lon-<lb/>gae, 3 p. </s>
  <s xml:id="echoid-s786" xml:space="preserve">latae, conſiſtunt.</s>
  <s xml:id="echoid-s787" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s788" xml:space="preserve">2. </s>
  <s xml:id="echoid-s789" xml:space="preserve">A latere cuiuslibet rotae facta eſt rota dentata CC <lb/>diam. </s>
  <s xml:id="echoid-s790" xml:space="preserve">20 p. </s>
  <s xml:id="echoid-s791" xml:space="preserve">dentes 60 pectinatim gerens. </s>
  <s xml:id="echoid-s792" xml:space="preserve">quibus du-<lb/>plex tympanum C et D gyratur. </s>
  <s xml:id="echoid-s793" xml:space="preserve">in priore baculi uerti-<lb/>cem ſpectant, in poſteriore ſunt horizonti paralleli. <lb/></s>
  <s xml:id="echoid-s794" xml:space="preserve">iſtud habet diametrum 4 p. </s>
  <s xml:id="echoid-s795" xml:space="preserve">hoc diam. </s>
  <s xml:id="echoid-s796" xml:space="preserve">3 p. </s>
  <s xml:id="echoid-s797" xml:space="preserve">4 dig.</s>
  <s xml:id="echoid-s798" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s799" xml:space="preserve">3. </s>
  <s xml:id="echoid-s800" xml:space="preserve">Motum tympani horizontalis ſequitur rota EF <lb/>diam. </s>
  <s xml:id="echoid-s801" xml:space="preserve">7 {1/2} p. </s>
  <s xml:id="echoid-s802" xml:space="preserve">inſtructa dentibus 40, iterumque mouens <lb/>tympanum G, cui annexum eſt manubrium ferreum, <lb/>craſſ<unsure/>um 4 dig. </s>
  <s xml:id="echoid-s803" xml:space="preserve">et recuruum H. </s>
  <s xml:id="echoid-s804" xml:space="preserve">Curuatura prominet <lb/>1 p. </s>
  <s xml:id="echoid-s805" xml:space="preserve">nec tamen omnino facta eſt ad angulos rectos, ſed <lb/>ad obliquos, ne embolinimio affrictu impediantur. </s>
  <s xml:id="echoid-s806" xml:space="preserve">em-<lb/>boli Q, adducuntur longuriis ferreis, (male in lonche-
<pb o="40" file="0050" n="50" rhead="CAPVT II."/>
rii libro p. </s>
  <s xml:id="echoid-s807" xml:space="preserve">177. </s>
  <s xml:id="echoid-s808" xml:space="preserve">catenae flexiles pinguntur) qui 5 dig. </s>
  <s xml:id="echoid-s809" xml:space="preserve">la-<lb/>ti, 1 {1/2} dig. </s>
  <s xml:id="echoid-s810" xml:space="preserve">ſpiſſi ſunt. </s>
  <s xml:id="echoid-s811" xml:space="preserve">et in medio uectes parui affiguntur, <lb/>ne longa nimis ferra curuentur.</s>
  <s xml:id="echoid-s812" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s813" xml:space="preserve">4. </s>
  <s xml:id="echoid-s814" xml:space="preserve">Antliarum huius machinae compoſitio ſingula-<lb/>ris, figura 12 Tab. </s>
  <s xml:id="echoid-s815" xml:space="preserve">2. </s>
  <s xml:id="echoid-s816" xml:space="preserve">exhibetur. </s>
  <s xml:id="echoid-s817" xml:space="preserve">Sunt nimirum dupli-<lb/>ces aſpirantes et inuerſae. </s>
  <s xml:id="echoid-s818" xml:space="preserve">ABCD eſt receptaculum <lb/>aquarum quernum, longum 4 {1/2} p, altum 3 p. </s>
  <s xml:id="echoid-s819" xml:space="preserve">ſub eo-<lb/>dem ſunt tres cylindri EF, EF, EF, ferrei ex quibus <lb/>aliae fiſtulae plumbeae in flumen continuantur. </s>
  <s xml:id="echoid-s820" xml:space="preserve">diame-<lb/>ter cylindrorum eſt 6 dig. </s>
  <s xml:id="echoid-s821" xml:space="preserve">ſupra hos tres ſimiles cylin-<lb/>dri cuprei IH, IH, IH, fulcro innituntur, eiusdem dia-<lb/>metri 6 dig. </s>
  <s xml:id="echoid-s822" xml:space="preserve">longi 2 {1/2} p. </s>
  <s xml:id="echoid-s823" xml:space="preserve">infra aperti, ſuperiore extremo <lb/>ualuulas habent, et connectuntur tubis recuruis tribus, <lb/>qui tandem in fiſtulam M cupream, quae aquas in ſu-<lb/>premum receptaculum auehit, deſinunt. </s>
  <s xml:id="echoid-s824" xml:space="preserve">tribus ſuperio-<lb/>ribus cylindris aptati ſunt emboli inuerſi, qui rectangu-<lb/>lis LK ducuntur, et his inferius adhaerent emboli aſpi-<lb/>rantes EE, cylindrorum inferiorum. </s>
  <s xml:id="echoid-s825" xml:space="preserve">Cum itaque ad-<lb/>ducitur rectangulum, trahuntur ſurſum quoque embo-<lb/>li, et ſic antlia aſpirans aquas haurit, premens eas in fi-<lb/>ſtulam M protrudit, quando nimirum cylindrorum ſu-<lb/>periorum ora inferiora H, H, H, aquis ſtagnantibus im-<lb/>merſa ſunt, ut reducto embolo eaedem in cylindrum <lb/>ingrediantur. </s>
  <s xml:id="echoid-s826" xml:space="preserve">Non autem una omnes leuantur embo-<lb/>li, ſed, dum duo deſcendunt, tertius aſcendit, prouti <lb/>manubrii curuati conditio poſtulat. </s>
  <s xml:id="echoid-s827" xml:space="preserve">Ceterum latitudo <lb/>rectanguli eſt 1 p. </s>
  <s xml:id="echoid-s828" xml:space="preserve">motus emboli fit in perpendiculo 18 <lb/>dig. </s>
  <s xml:id="echoid-s829" xml:space="preserve">receptaculum AB abeſt a ſuperficie aquarum 16 <lb/>uel 20 pedibus pro diuerſa fluminis altitudine. </s>
  <s xml:id="echoid-s830" xml:space="preserve">ſupre-<lb/>mum uero receptaculum, ex quo iterum aquae dela-<lb/>buntur, ultra aquas fluminis 18 ſexpedalibus perticis <lb/>remouetur.</s>
  <s xml:id="echoid-s831" xml:space="preserve"/>
</p>
<pb o="41" file="0051" n="51" rhead="DE MACHINIS HYDRAVL. PARISIENSIBVS."/>
<p>
  <s xml:id="echoid-s832" xml:space="preserve">5. </s>
  <s xml:id="echoid-s833" xml:space="preserve">Similem effectum praeſtat alterum tympanum D, <lb/>cuius manubrium curuatum tres libriles K, L, M, 12 p. <lb/></s>
  <s xml:id="echoid-s834" xml:space="preserve">longos, quibus tres emboli inuerſi adhaerent, mo-<lb/>uet. </s>
  <s xml:id="echoid-s835" xml:space="preserve">Axes autem horum intra cupreas patellas <lb/>uoluuntur.</s>
  <s xml:id="echoid-s836" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s837" xml:space="preserve">6. </s>
  <s xml:id="echoid-s838" xml:space="preserve">Rotae ſic ſuſpenſae ſunt, ut cum creſcit uel de-<lb/>creſcit flumen, attolli et demitti intra columnas pos-<lb/>ſint. </s>
  <s xml:id="echoid-s839" xml:space="preserve">Quem in finem in ſingulis angulis pancratia col-<lb/>locata, et in tignis ſiue columnis, quae rotam ſuſten-<lb/>tant, interuallo nouem digitorum ſoramina facta ſunt, <lb/>in quae claui ferrei immittuntur, ex quibus tota rotac <lb/>moles pendet. </s>
  <s xml:id="echoid-s840" xml:space="preserve">Quin uerſus ſuperiorem quoque con-<lb/>tignationem rota adducitur, quando glacies in flumi-<lb/>ne natant, aut quando idem nimis altum exiſtit.</s>
  <s xml:id="echoid-s841" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s842" xml:space="preserve">7. </s>
  <s xml:id="echoid-s843" xml:space="preserve">Inſuper rotam dentatam EF cingit circulus ligneus, <lb/>qui cochlea adducitur, et laxatur, ut hoc tanquam freno <lb/>omnis cohiberi motus queat. </s>
  <s xml:id="echoid-s844" xml:space="preserve">Aquae, quae ob aluei mu-<lb/>ro ſolido utrimque clauſi anguſtiam, per totam urbem <lb/>maiore celeritate ruunt, paulo uelociores redduntur, <lb/>dum ſuper palos ante pontem infixos uoluuntur. </s>
  <s xml:id="echoid-s845" xml:space="preserve">Verum <lb/>ante rotas cataractae demittuntur, quae nimium aqua-<lb/>rum affluxum moderantur. </s>
  <s xml:id="echoid-s846" xml:space="preserve">Quae autem de una rota <lb/>dixi, ualent etiam de altera, quae alterius prorſus ſi-<lb/>milis eſt.</s>
  <s xml:id="echoid-s847" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s848" xml:space="preserve">8. </s>
  <s xml:id="echoid-s849" xml:space="preserve">Supereſt, ut quantum aquarum his duabus rotis, <lb/>intra 24 horarum ſpatium in receptaculum inferatur, <lb/>et quae uis totam machinam moueat, explicemus, <lb/>Vtemur hic Ioncherii obſeruationibus et experimentis. <lb/></s>
  <s xml:id="echoid-s850" xml:space="preserve">hypotheſes ſunt 1. </s>
  <s xml:id="echoid-s851" xml:space="preserve">rotam bis gyrari intra temporis minu-<lb/>tum. </s>
  <s xml:id="echoid-s852" xml:space="preserve">2. </s>
  <s xml:id="echoid-s853" xml:space="preserve">machinam integram et ſine uitio eſſe, cete-<lb/>ra ex ſuperioribus petantur. </s>
  <s xml:id="echoid-s854" xml:space="preserve">Motus nempe emboli eſt <lb/>in perpendiculo 18 digitorum, et columna aquae tali <lb/>motu hauſta, capit 18 cantharos Pariſienſes, quando
<pb o="42" file="0052" n="52" rhead="CAPVT II."/>
antliae cylindrus habet diametrum 8 digitorum, 12 can-<lb/>tharis aequipollet in cylindro 6 dig. </s>
  <s xml:id="echoid-s855" xml:space="preserve">6. </s>
  <s xml:id="echoid-s856" xml:space="preserve">lin. </s>
  <s xml:id="echoid-s857" xml:space="preserve">10 cantharis <lb/>in cylindro 6 dig. </s>
  <s xml:id="echoid-s858" xml:space="preserve">(ſunt enim hi cylindri inaequales) <lb/>Verum quia tympana ad rotas dentatas habent diuer-<lb/>ſam rationem, (nempe C 20 D 15 baculos gerit, et <lb/>rotae EF 40 dentium, tympanum G 20 dentium re-<lb/>ſpondet, quare tympanum D, una rotae conuerſione <lb/>quater, obrationem 15: </s>
  <s xml:id="echoid-s859" xml:space="preserve">60, et tympanam C, et rota EF <lb/>ei iuncta, tantumter, ob rationem 20: </s>
  <s xml:id="echoid-s860" xml:space="preserve">60 circumagitur, <lb/>ſed tympanum G eodem tempore ſexies conuertitur, <lb/>ob rationem compoſitam, 2 et 3.) </s>
  <s xml:id="echoid-s861" xml:space="preserve">hinc ſex emboli una <lb/>rotae uertigine ſexies, reliqui ſex tantum quater in aquas <lb/>propellendas impetum faciunt.</s>
  <s xml:id="echoid-s862" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s863" xml:space="preserve">9. </s>
  <s xml:id="echoid-s864" xml:space="preserve">Ex antliis 6, quae ſexies trudunt aquas, duae ha-<lb/>bent diam. </s>
  <s xml:id="echoid-s865" xml:space="preserve">8. </s>
  <s xml:id="echoid-s866" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s867" xml:space="preserve">una 6 {1/2} dig. </s>
  <s xml:id="echoid-s868" xml:space="preserve">tres 6 dig. </s>
  <s xml:id="echoid-s869" xml:space="preserve">et attollunt 478 <lb/>cantharos. </s>
  <s xml:id="echoid-s870" xml:space="preserve">ſex reliquarum, quae quater agunt, dumro-<lb/>ta ſemel uoluitur, una eſt 8 dig. </s>
  <s xml:id="echoid-s871" xml:space="preserve">quinque 6 {1/2} dig. </s>
  <s xml:id="echoid-s872" xml:space="preserve">et hau-<lb/>riunt 36 cantharos. </s>
  <s xml:id="echoid-s873" xml:space="preserve">ſumma eſt 794 canth. </s>
  <s xml:id="echoid-s874" xml:space="preserve">et ſic uno <lb/>minuto, quo bis rota in orbem it, 1588 canthari, et fa-<lb/>cta multiplicatione per 60, intra horam 95280 canthari, <lb/>intra 24 horas 2286720 canthari, in receptaculum ege-<lb/>runtur, h. </s>
  <s xml:id="echoid-s875" xml:space="preserve">e. </s>
  <s xml:id="echoid-s876" xml:space="preserve">diuiſione per 280 facta, 8167 dolia.</s>
  <s xml:id="echoid-s877" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s878" xml:space="preserve">10. </s>
  <s xml:id="echoid-s879" xml:space="preserve">Aquae in receptaculo plumbeo effuſae, non <lb/>immediate relabuntur per canal@@ ſuos, ſed percolan-<lb/>tur per exiguas fiſtulas conicas, ac deinceps puriores <lb/>redditae in ſparſos per urbem fonticulos diffundun-<lb/>tur.</s>
  <s xml:id="echoid-s880" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s881" xml:space="preserve">11. </s>
  <s xml:id="echoid-s882" xml:space="preserve">Quod autem attinet uires, quibus a fiuminis im-<lb/>petu machina inſtruitur, de iis ſequentia non abs re <lb/>erit notaſſe. </s>
  <s xml:id="echoid-s883" xml:space="preserve">Sequana, quae per Lutetiam Pariſiorum <lb/>fluit, altis ripis muro firmatis clauditur, uelocius <lb/>hic currit, quam in alueo libero, et experimentis fa-<lb/>ctis conſtitit, flumen a ponte B. </s>
  <s xml:id="echoid-s884" xml:space="preserve">Virginis usque ad
<pb o="43" file="0053" n="53" rhead="DE MACHINIS HYDRAVL. PARISIENSIB."/>
pontem regium, quadruplo celerius eſſe, quam inter <lb/>hunc ultimum pontem, et ripam hoſpitio inualidorum <lb/>militum extra urbem oppoſitam, etiamſi utrimque fe-<lb/>re aequales ſint diſtantiae. </s>
  <s xml:id="echoid-s885" xml:space="preserve">Hinc Ioncherius p. </s>
  <s xml:id="echoid-s886" xml:space="preserve">173. <lb/></s>
  <s xml:id="echoid-s887" xml:space="preserve">colligit, celeritatem 12 p. </s>
  <s xml:id="echoid-s888" xml:space="preserve">pro uno minuto ſecundo <lb/>temporis. </s>
  <s xml:id="echoid-s889" xml:space="preserve">Si autem ponamus, rotae alam unam <lb/>perpendiculari impetu pelli, aut impetus in duas ob-<lb/>lique factos tantundem ualere, a priſmate aqueo cuius <lb/>baſis eſt area alae, nempe 54 ſiue 3. </s>
  <s xml:id="echoid-s890" xml:space="preserve">18 pedum quadra-<lb/>torum, altitudo 3 p. </s>
  <s xml:id="echoid-s891" xml:space="preserve">erunt ergo 162 p. </s>
  <s xml:id="echoid-s892" xml:space="preserve">cubici hoc pri-<lb/>ſmate contenti. </s>
  <s xml:id="echoid-s893" xml:space="preserve">quilibet cubicus pes aeſtimatur 70 l. </s>
  <s xml:id="echoid-s894" xml:space="preserve"><lb/>Pariſ. </s>
  <s xml:id="echoid-s895" xml:space="preserve">et 162 = 11340 lib. </s>
  <s xml:id="echoid-s896" xml:space="preserve">Hoc pondus multum iuua-<lb/>tur uectibus perpetuis rotarum et tympanorum. </s>
  <s xml:id="echoid-s897" xml:space="preserve">ut <lb/>ſciatur, qualis ſit facultas dati pond eris prope rotam <lb/>dentatam, infer; </s>
  <s xml:id="echoid-s898" xml:space="preserve">(poſita rota 20 p. </s>
  <s xml:id="echoid-s899" xml:space="preserve">diam. </s>
  <s xml:id="echoid-s900" xml:space="preserve">cum Ionche-<lb/>rio) ut 5 {1/2} diſtantia dentiuma centro, ſiue ſemidiameter <lb/>rotae dentatae, ad 8 {1/2} ſemidiametrum rotae, ita 11340 lib. </s>
  <s xml:id="echoid-s901" xml:space="preserve"><lb/>ad 17525 {5/11} lib. </s>
  <s xml:id="echoid-s902" xml:space="preserve">Dentes agunt tympana duo alterum 2 p. </s>
  <s xml:id="echoid-s903" xml:space="preserve">9 <lb/>dig. </s>
  <s xml:id="echoid-s904" xml:space="preserve">diam. </s>
  <s xml:id="echoid-s905" xml:space="preserve">cui inſunt fuſi ſiue baculi 15, et hoc manu-<lb/>brium 9 dig. </s>
  <s xml:id="echoid-s906" xml:space="preserve">torquet, h. </s>
  <s xml:id="echoid-s907" xml:space="preserve">e, ratio radii tympani ad ra-<lb/>dium manubrii eſt 33 ad 18. </s>
  <s xml:id="echoid-s908" xml:space="preserve">infer, ut diſtantia oneris ab <lb/>hypomochlio, ſiue radius manubrii, ad diſtantiam ui-<lb/>rium ab eodem, ſiue radium tympani, ſic uis huic ap-<lb/>plicita 17525 lib. </s>
  <s xml:id="echoid-s909" xml:space="preserve">ad uim qua agitur manubrium 32130 <lb/>lib. </s>
  <s xml:id="echoid-s910" xml:space="preserve">Hoc manubrium mouet 3 embolos, ex quibus <lb/>duo ſemper premunt unus 8 dig. </s>
  <s xml:id="echoid-s911" xml:space="preserve">alter 6 {1/2} dig. </s>
  <s xml:id="echoid-s912" xml:space="preserve">diam. </s>
  <s xml:id="echoid-s913" xml:space="preserve">et <lb/>aquea columna in fiſtula usque ad receptaculum 95 p. </s>
  <s xml:id="echoid-s914" xml:space="preserve"><lb/>alta, grauis eſt 3808 l. </s>
  <s xml:id="echoid-s915" xml:space="preserve">quae grauitas ob affrictum par-<lb/>tium, et pondus earum duplicatur, 7616 l. </s>
  <s xml:id="echoid-s916" xml:space="preserve">et quia non <lb/>eadem ſemper impetus aquarum poteſtas eſt, et aquae <lb/>poſt alam parumper conſiſtunt, nec pulſus in alas fiunt <lb/>perpendiculariter, iterum duplum ſumere ſatius uide-
<pb o="44" file="0054" n="54" rhead="CAPVT II."/>
tur, nempe 15232 l. </s>
  <s xml:id="echoid-s917" xml:space="preserve">quo ſublato ex ui 32130, ſuperſunt <lb/>16898 l. </s>
  <s xml:id="echoid-s918" xml:space="preserve">pro tympano altero.</s>
  <s xml:id="echoid-s919" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s920" xml:space="preserve">12. </s>
  <s xml:id="echoid-s921" xml:space="preserve">Tympanum G habet fuſos 20, rota EF dentes <lb/>40; </s>
  <s xml:id="echoid-s922" xml:space="preserve">et talis eſt etiam ratio peripheriarum. </s>
  <s xml:id="echoid-s923" xml:space="preserve">uires autem <lb/>ac pondera ſunt in reciproca ratione ſpatiorum per <lb/>quae mouentur §. </s>
  <s xml:id="echoid-s924" xml:space="preserve">29. </s>
  <s xml:id="echoid-s925" xml:space="preserve">Inſtit. </s>
  <s xml:id="echoid-s926" xml:space="preserve">mechan. </s>
  <s xml:id="echoid-s927" xml:space="preserve">quare inf. </s>
  <s xml:id="echoid-s928" xml:space="preserve">40 ad 20 <lb/>h. </s>
  <s xml:id="echoid-s929" xml:space="preserve">e. </s>
  <s xml:id="echoid-s930" xml:space="preserve">2:</s>
  <s xml:id="echoid-s931" xml:space="preserve">1 ita uis 16898 ad 8449 lib. </s>
  <s xml:id="echoid-s932" xml:space="preserve">quae mouent tympa-<lb/>num G. </s>
  <s xml:id="echoid-s933" xml:space="preserve">radii uero huius et manubrii ratio eſt 22:</s>
  <s xml:id="echoid-s934" xml:space="preserve">9. </s>
  <s xml:id="echoid-s935" xml:space="preserve">inf. <lb/></s>
  <s xml:id="echoid-s936" xml:space="preserve">9:</s>
  <s xml:id="echoid-s937" xml:space="preserve">22 ita 8449 ad 20653 {1/9} lib. </s>
  <s xml:id="echoid-s938" xml:space="preserve">leuanda autem eſt columna <lb/>aquea 95 p. </s>
  <s xml:id="echoid-s939" xml:space="preserve">alta 6 {1/2} dig. </s>
  <s xml:id="echoid-s940" xml:space="preserve">diametr. </s>
  <s xml:id="echoid-s941" xml:space="preserve">cuius pondus 2839 li-<lb/>brar. </s>
  <s xml:id="echoid-s942" xml:space="preserve">uel duplum, ob uaria motus obſtacula 5676 lib. </s>
  <s xml:id="echoid-s943" xml:space="preserve"><lb/>cui uis 20653 lib. </s>
  <s xml:id="echoid-s944" xml:space="preserve">omnino par eſt, etiamſi duplo et am-<lb/>plius onus mouendum ſupereſſet. </s>
  <s xml:id="echoid-s945" xml:space="preserve">Atque ita etiam de <lb/>alterius rotae actione et uiribus ac oneribus, quae mo-<lb/>uentur, eſt iudicandum.</s>
  <s xml:id="echoid-s946" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s947" xml:space="preserve">13. </s>
  <s xml:id="echoid-s948" xml:space="preserve">Altera machina hydraulica, cuius inſignis utilitas <lb/>Pariſiis ſpectatur, eſt poſt pontem nouum, et Samaritana <lb/>uocatur, a ſtatuis optimi Seruatoris et Samaritidis, <lb/>quae, iuxta receptaculum aquarum lapideum ſuper <lb/>ponte erectae ſunt. </s>
  <s xml:id="echoid-s949" xml:space="preserve">Simpliciſſima et propterea per-<lb/>quam commoda eius conſtructio ſequenti modo ſeſe <lb/>habet. </s>
  <s xml:id="echoid-s950" xml:space="preserve">Rota unica intra palos in fundum adactos, pau-<lb/>lo ultra medium pontem eo loco ſuſpenſa eſt, quo cur-<lb/>ſus fluminis dirigitur, 20 p. </s>
  <s xml:id="echoid-s951" xml:space="preserve">diametri, lata 18 p. </s>
  <s xml:id="echoid-s952" xml:space="preserve">alae im-<lb/>poſitae in interna peripheria latae ſunt 3 {1/2} p. </s>
  <s xml:id="echoid-s953" xml:space="preserve">exaxe li-<lb/>gneo prominent curua manubria, quorum reflexum <lb/>brachium eſt 2 p. </s>
  <s xml:id="echoid-s954" xml:space="preserve">longum. </s>
  <s xml:id="echoid-s955" xml:space="preserve">Vnum eorum trahit tigna <lb/>tria librantia, in medio ex axe ſuſpenſa, 18 uel 20 p. <lb/></s>
  <s xml:id="echoid-s956" xml:space="preserve">longa, quorum altero extremo adhaere<unsure/>nt tres emboli <lb/>inuerſi; </s>
  <s xml:id="echoid-s957" xml:space="preserve">alterum manubrium tantum duos eiusmodi li-<lb/>briles cum embolis mouet. </s>
  <s xml:id="echoid-s958" xml:space="preserve">Manubria ad rectos angu-<lb/>los inflexa ſunt, quia longa admodum ſunt ferra, quae <lb/>embolos ducunt. </s>
  <s xml:id="echoid-s959" xml:space="preserve">Emboli ſunt ſpiſſiores, ab una par-
<pb o="45" file="0055" n="55" rhead="DE MACHINIS HYDRAVL. PARISIENSIB. 45"/>
te 11 dig. </s>
  <s xml:id="echoid-s960" xml:space="preserve">ab altera 9 dig. </s>
  <s xml:id="echoid-s961" xml:space="preserve">4 lin. </s>
  <s xml:id="echoid-s962" xml:space="preserve">diametri. </s>
  <s xml:id="echoid-s963" xml:space="preserve">motus eorum fit <lb/>in perpendiculo 3 {1/2} p. </s>
  <s xml:id="echoid-s964" xml:space="preserve">uel 3 {3/4} p. </s>
  <s xml:id="echoid-s965" xml:space="preserve">Machina intra 4 colu-<lb/>mnas, uti prior prope pontem B. </s>
  <s xml:id="echoid-s966" xml:space="preserve">Virginis ſuſpenſa, <lb/>demittitur et attollitur, prout aquarum altitudo po-<lb/>ſtulat. </s>
  <s xml:id="echoid-s967" xml:space="preserve">Receptaculum, in quo aquae colliguntur, ab <lb/>antliis 71 pedibus diſtat.</s>
  <s xml:id="echoid-s968" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s969" xml:space="preserve">14. </s>
  <s xml:id="echoid-s970" xml:space="preserve">Motus rotae bis intra minutum primum, ab-<lb/>ſoluitur, columnae duae ab una parte, diam. </s>
  <s xml:id="echoid-s971" xml:space="preserve">9 {1/3} dig. <lb/></s>
  <s xml:id="echoid-s972" xml:space="preserve">altae 3 p. </s>
  <s xml:id="echoid-s973" xml:space="preserve">{3/4}, capiunt 131 {3/4} cantharos, columnae tres <lb/>a parte oppoſita diam. </s>
  <s xml:id="echoid-s974" xml:space="preserve">11 dig. </s>
  <s xml:id="echoid-s975" xml:space="preserve">altae 3 {1/2} p. </s>
  <s xml:id="echoid-s976" xml:space="preserve">complectuntur <lb/>242 {2/3} cantharos. </s>
  <s xml:id="echoid-s977" xml:space="preserve">ſumma eſt 374 {5/12} canth. </s>
  <s xml:id="echoid-s978" xml:space="preserve">qui uno cir-<lb/>cumactu rotae hauriuntur, ergo intra minutum 748 {5/0} <lb/>et hora una, 44930. </s>
  <s xml:id="echoid-s979" xml:space="preserve">per 24 h. </s>
  <s xml:id="echoid-s980" xml:space="preserve">1078320 ſiue 3851 dolia Pa-<lb/>riſienſia.</s>
  <s xml:id="echoid-s981" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s982" xml:space="preserve">15. </s>
  <s xml:id="echoid-s983" xml:space="preserve">Celeritas fluminis ſimilis eſt illius, quae obſer-<lb/>uatur prope pontem B. </s>
  <s xml:id="echoid-s984" xml:space="preserve">V. </s>
  <s xml:id="echoid-s985" xml:space="preserve">ſiue 12 p. </s>
  <s xml:id="echoid-s986" xml:space="preserve">uno ſecundo mi-<lb/>nuto. </s>
  <s xml:id="echoid-s987" xml:space="preserve">Si ponatur unus aſſer alae, 18 p. </s>
  <s xml:id="echoid-s988" xml:space="preserve">longae 3 {1/2} la-<lb/>tae, perpendiculariter impulſus, ſuper area alae, ſiue <lb/>pedibus quadratis 63, totidem pedes cubici aquarum <lb/>conſiſtunt, ſed triplum eſt 189, et ſingulorum pondus <lb/>70, ergo pondus totum 13230 l. </s>
  <s xml:id="echoid-s989" xml:space="preserve">quod iuuatur radio ro-<lb/>tae, et pro quantitate infer, ut 2 p. </s>
  <s xml:id="echoid-s990" xml:space="preserve">manubrii ad 8 {3/12} <lb/>p. </s>
  <s xml:id="echoid-s991" xml:space="preserve">rad. </s>
  <s xml:id="echoid-s992" xml:space="preserve">rotae usque ad alam mediam, ita 13230 ad 54573 {3/4}. <lb/></s>
  <s xml:id="echoid-s993" xml:space="preserve">haec uis eleuare debet duas columnas aquae, quarum <lb/>pondus eſt 12378 l. </s>
  <s xml:id="echoid-s994" xml:space="preserve">ſiue duplum potius, ut machinae <lb/>obſtacula ſuperentur 24786 l. </s>
  <s xml:id="echoid-s995" xml:space="preserve">ſed cum duplo et ampli-<lb/>us excedat potentia onus mouendum, non eſt dubium, <lb/>machinam etiam humiliore flumine continuo officium <lb/>ſuum exſecuturan@.</s>
  <s xml:id="echoid-s996" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s997" xml:space="preserve">16. </s>
  <s xml:id="echoid-s998" xml:space="preserve">His machinis aquae ingeruntur in quinqua-<lb/>ginta caſtella publica (fontaines) quae in uſum atque <lb/>ornamentum urbis regiae paſſim diſpoſita uiſuntur. <lb/></s>
  <s xml:id="echoid-s999" xml:space="preserve">ſunt tamen inter eadem nonnulla, quae replentur aquis
<pb o="46" file="0056" n="56" rhead="CAPVT III."/>
ſuper aquaeductu Arcelienſi, ex uilla Rungis, quae <lb/>duabus leucis Lutetia abeſt, in palatium regium, quod <lb/>Luxenburgicum uocatur, deriuatis. </s>
  <s xml:id="echoid-s1000" xml:space="preserve">lſte aquaeductus <lb/>inter pulcherrima et ſplendidiſſima, quibus ager Pari-<lb/>ſienſis condecoratus eſt, opera non ultimo loco cenſeri <lb/>meretur. </s>
  <s xml:id="echoid-s1001" xml:space="preserve">Condidit eum Maria Medicea, Ludouici <lb/>XIII mater. </s>
  <s xml:id="echoid-s1002" xml:space="preserve">Tradunt Galli, iam olim ſuper uallem <lb/>Arcelienſem aquas a I<unsure/>uliano Caeſare, qui apoſtatae co-<lb/>gnomine notatur, ſimili ſuper muro deductas fuiſſe in pa-<lb/>latium imperatoris, cuius hodienum rudera in aedi-<lb/>bus cluniacenſibus monſtrantur.</s>
  <s xml:id="echoid-s1003" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div14" type="section" level="1" n="10">
<head xml:id="echoid-head22" xml:space="preserve">CAPVT III. <lb/>DE <lb/>DV ABVS MOLETRINIS <lb/>HYDRAVLICIS <lb/>QVARVM ALAE VENTO VERSANTVR.</head>
<head xml:id="echoid-head23" xml:space="preserve">I.</head>
<p>
  <s xml:id="echoid-s1004" xml:space="preserve">Non deſunt machinae hydraulicae auxilio uento-<lb/>rum animatae. </s>
  <s xml:id="echoid-s1005" xml:space="preserve">Hollandi inprimis frequen-<lb/>tiſſimas in pratis ſuis conſtitutas habent, qui-<lb/>bus aquas e canalibus redundantes, per riuos <lb/>eodem reducunt. </s>
  <s xml:id="echoid-s1006" xml:space="preserve">Sed eaedem ſimplices admodum <lb/>ſunt, et ad perexiguam altitudinem aquas euchunt. <lb/></s>
  <s xml:id="echoid-s1007" xml:space="preserve">ſiquidem alae rotae 1 {1/2} p. </s>
  <s xml:id="echoid-s1008" xml:space="preserve">latae, 2 p. </s>
  <s xml:id="echoid-s1009" xml:space="preserve">longae, ad rectos
<pb o="47" file="0057" n="57" rhead="DE MOLIS ALATIS HYDRAVLICIS."/>
angulos ſuper peripheria poſitae, aquas obvias tantum <lb/>ſupra planum inclinatum aſſeribus ueſtitum, et tres <lb/>circiter pedes ſuperficie aquarum altius, protrudunt, <lb/>atque in foſſas eiiciunt, ex quibus tandem in amplio-<lb/>res alueos deuoluuntur, atque ita breui tempore, a ma-<lb/>gna aquarum ui nullo fere negotio humiliora prata ſua <lb/>liberant. </s>
  <s xml:id="echoid-s1010" xml:space="preserve">Verum opera, quae altius tollunt aquas, uen-<lb/>to commota, non adeo magno numero exſtructa ſunt, <lb/>partim quia aura non ſemper fauet, partim quia uis at-<lb/>que impetus uentorum raro aequabilitatem ſeruare ſo-<lb/>let <anchor type="note" xlink:href="" symbol="(*)"/>. </s>
  <s xml:id="echoid-s1011" xml:space="preserve">Cum itaque repererim duas molas hydraulicas,
prope arcem regiam Meudon, haud procul Pariſiis ſi-<lb/>tam, quarum uſu probata fabrica eſt, nolui earum de-<lb/>ſcriptionem, quippe a nemine hactenus datam, omit-<lb/>tere. </s>
  <s xml:id="echoid-s1012" xml:space="preserve">Scalam tamen non adieci, chartae ſumtibusque <lb/>parſurus, ſufficere exiſtimans, ſi menſurae fideliter in-<lb/>dicarentur.</s>
  <s xml:id="echoid-s1013" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1014" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1015" xml:space="preserve">Exſtructae ſunt moletrinae, de quibus agere <lb/>inſtitui, circa finem uiuarii Meldoniani in montis, cui <lb/>impoſita eſt arx, ſummo, quod in planitiem amoenam <lb/>deſinit, e regione uillae, quae Villebon nominatur. <lb/></s>
  <s xml:id="echoid-s1016" xml:space="preserve">Huc aquae pluuiae, et fontium uicinorum, per riuos <lb/>in ampliſſimum ſtagnum colliguntur, et ex hoc ſtagno, <lb/>
<anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/>
<pb o="48" file="0058" n="58" rhead="CAPVT III."/>
ad puteos, quibus molae imminent, aquaeductibus, <lb/>ſiue canalibus ſubterraneis perueniunt.</s>
  <s xml:id="echoid-s1017" xml:space="preserve"/>
</p>
<div xml:id="echoid-div14" type="float" level="2" n="1">
<note position="foot" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">(*) <emph style="sc">Georg</emph>. <emph style="sc">Andr</emph>. <emph style="sc">Boecler</emph> in theatro machinarum <lb/>nouo f. 45. fig. 117. molam alatam, roſario hydraulico, <lb/>quod dicitur, agitando idoneam, ſequentem in mo-<lb/>dum compenere docer. Axis nempe alis inſtructus ge-<lb/>ſtat rotam dentatam uerticalem, haec tympanum et <lb/>aliam rotam dentatam horizonti parallelam in orbem <lb/>agit, atque ita, cum ſubiecto rotae huic tympano, <lb/>globi lignei ex fune uel catena ſuſpenſi, et interuallo, <lb/>quod diametro globi cuiuslibet par eſt, diſtincti, per <lb/>cylindrum cauum, infra nonnihil in aquas demerſum, <lb/>ducuntur, et aquae una attolluntur.</note>
</div>
<p>
  <s xml:id="echoid-s1018" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1019" xml:space="preserve">Moletrina, quae uenientibus Meldono prior occur-<lb/>
<anchor type="note" xlink:label="note-0058-01a" xlink:href="note-0058-01"/>
rit, et iuxta quam molitoris aedes ſunt, repraeſentatur <lb/>fig. </s>
  <s xml:id="echoid-s1020" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1021" xml:space="preserve">et ſequentem membrorum conformationem ha-<lb/>bet. </s>
  <s xml:id="echoid-s1022" xml:space="preserve">Axis ligneus A ſuſtinet alas quatuor, quarum ra-<lb/>dii 24 pedes longiſunt. </s>
  <s xml:id="echoid-s1023" xml:space="preserve">componuntur autem iidem dua-<lb/>bus ex partibus. </s>
  <s xml:id="echoid-s1024" xml:space="preserve">brachia craſſiora in axis cylindro fir-<lb/>mata fortiora exiſtunt, nempe 15 dig. </s>
  <s xml:id="echoid-s1025" xml:space="preserve">ſpiſſa, his alia <lb/>incumbunt graciliora 8 dig. </s>
  <s xml:id="echoid-s1026" xml:space="preserve">in quibus regulae tranſuer-<lb/>ſae, ſiue baculi, 7 p. </s>
  <s xml:id="echoid-s1027" xml:space="preserve">longi pro uelis geſtandis immit-<lb/>tuntur. </s>
  <s xml:id="echoid-s1028" xml:space="preserve">Intra axem ligneum tanquam modiolum fer-<lb/>reus eſt, quem alae in orbem uertunt, nititur gemino <lb/>fulcro quadratis paruis ſubiectis ſignificato. </s>
  <s xml:id="echoid-s1029" xml:space="preserve">craſſus eſt <lb/>anteriore parte 7 dig. </s>
  <s xml:id="echoid-s1030" xml:space="preserve">poſteriore 6 dig. </s>
  <s xml:id="echoid-s1031" xml:space="preserve">longitudo eius <lb/>6 p. </s>
  <s xml:id="echoid-s1032" xml:space="preserve">curuatur in medio ad rectos angulos, perpendicu-<lb/>lum reflexum eſt 10 dig. </s>
  <s xml:id="echoid-s1033" xml:space="preserve">mouetur intra patinas cupreas, <lb/>ne incendium efficiat attritus ferri celerrimus. </s>
  <s xml:id="echoid-s1034" xml:space="preserve">ab hoc <lb/>axe pendet truncus ferreus BHQ cuius extremo B <lb/>cupreus orbis inſertus et ferreis marginibus conſtrictus <lb/>eſt, ob modo commemoratam rationem. </s>
  <s xml:id="echoid-s1035" xml:space="preserve">portio BH <lb/>eſt 3 p. </s>
  <s xml:id="echoid-s1036" xml:space="preserve">longa, eidemque in H annectitur tolleno, ſiue <lb/>uectis ligneus HIK, circa axem in I uolubilis, cuius <lb/>extremo impoſitum eſt pondus K 1500 librarum, eum <lb/>in finem, ut dum retrahend@ ſunt emboli, hoc ipſo <lb/>motus adiuuetur.</s>
  <s xml:id="echoid-s1037" xml:space="preserve"/>
</p>
<div xml:id="echoid-div15" type="float" level="2" n="2">
<note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">Fig. XIV. <lb/>Tab. IV.</note>
</div>
<p>
  <s xml:id="echoid-s1038" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1039" xml:space="preserve">Prope axem ligneum applicata eſt rota FG diam. <lb/></s>
  <s xml:id="echoid-s1040" xml:space="preserve">7 p. </s>
  <s xml:id="echoid-s1041" xml:space="preserve">quam ambit circulus ligneus, ligneis baculis, ne a <lb/>rota diſcedat, cohibitus, hic circulus ita aptatur, <lb/>ut ope uectis H Fig. </s>
  <s xml:id="echoid-s1042" xml:space="preserve">15, laxari et ad rotam adduci que-<lb/>
<anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
at. </s>
  <s xml:id="echoid-s1043" xml:space="preserve">quando enim laxatur plus minusue, rota liberius <lb/>uoluitur, quando autem conſtringitur, affrictu eius <lb/>celeritas motus temperatur, uel idem omnino ſiſtitur.</s>
  <s xml:id="echoid-s1044" xml:space="preserve">
<pb o="49" file="0059" n="59" rhead="DE MOLIS ALATIS HYDRAVLICIS."/>
Vocant ideo hunc circulum frenum, quo etiam alias <lb/>molitores, in ſimili caſu frequentius utuntur. </s>
  <s xml:id="echoid-s1045" xml:space="preserve">Figura <lb/>15 rem omnem clare ob oculos point. </s>
  <s xml:id="echoid-s1046" xml:space="preserve">B eſt rota, <lb/>quam ambit ille circulus ligneus, βγ catena, qua re-<lb/>tinetur, δγ ferrum, circa clauum in tigno fixum, mo-<lb/>bile, ηε uectis ipſe, Θ catena qua circa trochleam tra-<lb/>hitur. </s>
  <s xml:id="echoid-s1047" xml:space="preserve">cum enim adducitur extremum η, alterum ε<unsure/> de-<lb/>primitur et γ cum circulo attollitur et laxatur.</s>
  <s xml:id="echoid-s1048" xml:space="preserve"/>
</p>
<div xml:id="echoid-div16" type="float" level="2" n="3">
<note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">Fig. XV. <lb/>Tab. IV.</note>
</div>
<p>
  <s xml:id="echoid-s1049" xml:space="preserve">5. </s>
  <s xml:id="echoid-s1050" xml:space="preserve">Truncus HQ continuatur usque ad eam regio-<lb/>nem, qua ex eodem emboli ſuſpenduntur, procedit <lb/>autem inter tigna, quibus moletrina ſuſtentatur. </s>
  <s xml:id="echoid-s1051" xml:space="preserve">Ge-<lb/>rit ibidem ferra quinque praelonga LR, LY, etc. </s>
  <s xml:id="echoid-s1052" xml:space="preserve">hic <lb/>tantum tria potui exhibere, quia orthographiam inter-<lb/>nam, ſectione per mediam molam facta, depinxi. </s>
  <s xml:id="echoid-s1053" xml:space="preserve">in-<lb/>terim ichnographiam a, b, c, d, e reſpice, ubi 5 brachia <lb/>quae quatuor ferra, pro embolis prementibus, unum <lb/>pro aſpirante, portant, diſtinctius apparent. </s>
  <s xml:id="echoid-s1054" xml:space="preserve">unum un-<lb/>co M. </s>
  <s xml:id="echoid-s1055" xml:space="preserve">adhaerens, ducit et reducit embolum antliae <lb/>aſpirantis, quae ex puteo aquas in uas plumbeum P ele-<lb/>uat, unde in embolos antliarum prementium, pro iis-<lb/>dem humectandis (uid. </s>
  <s xml:id="echoid-s1056" xml:space="preserve">cap. </s>
  <s xml:id="echoid-s1057" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1058" xml:space="preserve">§. </s>
  <s xml:id="echoid-s1059" xml:space="preserve">8, circa fin.) </s>
  <s xml:id="echoid-s1060" xml:space="preserve">deſtillant. <lb/></s>
  <s xml:id="echoid-s1061" xml:space="preserve">reliqua ferra quatuor adhaerent extremis tignorum li-<lb/>brantium long. </s>
  <s xml:id="echoid-s1062" xml:space="preserve">8 p. </s>
  <s xml:id="echoid-s1063" xml:space="preserve">(balanciers) RS, XY, quae utroque <lb/>extremo mouent embolos prementes et aſpirantes, de <lb/>quorum actione ex praecedente capite abunde conſtat, <lb/>et his octo embolis aquae ex puteo eleuatae, in fiſtulas <lb/>magno impetu protruduntur.</s>
  <s xml:id="echoid-s1064" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1065" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1066" xml:space="preserve">Vt motus embolorum ſurſum deorſumque in li-<lb/>nea perpendiculari fiat, et affrictus euitetur, ſcapus <lb/>ferreus intra lighi Q cauum aſcendit et deſcendit.</s>
  <s xml:id="echoid-s1067" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1068" xml:space="preserve">7. </s>
  <s xml:id="echoid-s1069" xml:space="preserve">Motus embolorum in antliis fit in perpendiculo <lb/>2 pedum, aqua putei a librilibus abeſt 8 p. </s>
  <s xml:id="echoid-s1070" xml:space="preserve">profunda 10 <lb/>p. </s>
  <s xml:id="echoid-s1071" xml:space="preserve">diameter cylindri ferrei antliae cuiuslibet 6 dig. </s>
  <s xml:id="echoid-s1072" xml:space="preserve">ſin-
<pb o="50" file="0060" n="60" rhead="CAPVT III."/>
gulis antliis fiſtula ducens cuprea diam. </s>
  <s xml:id="echoid-s1073" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1074" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s1075" xml:space="preserve">reſpondet, <lb/>ſed mox duae in unam 6 dig. </s>
  <s xml:id="echoid-s1076" xml:space="preserve">onus ſuum ingerunt.</s>
  <s xml:id="echoid-s1077" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1078" xml:space="preserve">8. </s>
  <s xml:id="echoid-s1079" xml:space="preserve">Axis alae ſolo 24 p. </s>
  <s xml:id="echoid-s1080" xml:space="preserve">ſublimior eſt, aquae ſurgunt <lb/>in fiſtulis per perpendiculum 12 p. </s>
  <s xml:id="echoid-s1081" xml:space="preserve">deinceps in amplio-<lb/>res canales diam. </s>
  <s xml:id="echoid-s1082" xml:space="preserve">10 dig. </s>
  <s xml:id="echoid-s1083" xml:space="preserve">illapſae, per decliue ad rece-<lb/>ptaculum commune, 250 perticis ſexpedalibus a moletri-<lb/>na remotum, deuoluuntur.</s>
  <s xml:id="echoid-s1084" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1085" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1086" xml:space="preserve">Copia aquarum hac moletrina in altum propul-<lb/>ſarum ſic innoteſcit. </s>
  <s xml:id="echoid-s1087" xml:space="preserve">Conuertitur, cum pulſus uen-<lb/>torum ſunt mediocres, ala ter ſingulis minutis, et eo <lb/>tempore 8 cylindri aquarum, diam. </s>
  <s xml:id="echoid-s1088" xml:space="preserve">6 dig. </s>
  <s xml:id="echoid-s1089" xml:space="preserve">altid. </s>
  <s xml:id="echoid-s1090" xml:space="preserve">2 p. </s>
  <s xml:id="echoid-s1091" xml:space="preserve">aſ-<lb/>ſurgunt. </s>
  <s xml:id="echoid-s1092" xml:space="preserve">tales ſinguli capiunt 15. </s>
  <s xml:id="echoid-s1093" xml:space="preserve">cantharos, octo 120. <lb/></s>
  <s xml:id="echoid-s1094" xml:space="preserve">itaque intra minutum 360, horam 21600, diem ſ. </s>
  <s xml:id="echoid-s1095" xml:space="preserve">24 h. </s>
  <s xml:id="echoid-s1096" xml:space="preserve"><lb/>518400. </s>
  <s xml:id="echoid-s1097" xml:space="preserve">canthari, ſiue 1851 dolia Pariſienſia hauriuntur. </s>
  <s xml:id="echoid-s1098" xml:space="preserve"><lb/>Inde etiam qualiscunque u<unsure/>irium neceſſariarum aeſtima-<lb/>tio inſtitui poſſet, ſi de affrictu materiae melius nobis <lb/>conſtaret. </s>
  <s xml:id="echoid-s1099" xml:space="preserve">Verum ex ſupra traditis conſequitur lucu-<lb/>lentiſſime, hic nihil praeter ſuſpiciones et coniecturas <lb/>ex effectu deductas proferri poſſe. </s>
  <s xml:id="echoid-s1100" xml:space="preserve">Illud mihi relatum <lb/>eſt, uentum exiguum ad motum producendum non <lb/>ſufficere, et molitor impetuoſiorem imbecilliori prae-<lb/>fert, quia tum demtis uelis, tum adducto circulo tem-<lb/>peramentum celeritati ſtatim adhibere poteſt.</s>
  <s xml:id="echoid-s1101" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1102" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1103" xml:space="preserve">Quando autem uelociter agitantur emboli, tum <lb/>tantam uim preſſu ſuo exſerunt @t oportuerit fiſtulam <lb/>ferream 4 dig. </s>
  <s xml:id="echoid-s1104" xml:space="preserve">diam. </s>
  <s xml:id="echoid-s1105" xml:space="preserve">in principio illius, qua aquae col-<lb/>liguntur, erigere, per quam aer, repentinis hauſtibus <lb/>adductus, expellatur, ſiquidem alias fiſtularum iunctu-<lb/>ras frangi, uel machinae motum cohi<unsure/>beri, obſeruatio-<lb/>nibus compertum fuit. </s>
  <s xml:id="echoid-s1106" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s1107" xml:space="preserve"><emph style="sc">Mariotte</emph> l. </s>
  <s xml:id="echoid-s1108" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1109" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1110" xml:space="preserve">389.</s>
  <s xml:id="echoid-s1111" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1112" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1113" xml:space="preserve">Alterius moletrinae hydraulicae, prope ſtagnum <lb/>
<anchor type="note" xlink:label="note-0060-01a" xlink:href="note-0060-01"/>
erectae ſtructura ſequens eſt. </s>
  <s xml:id="echoid-s1114" xml:space="preserve">v. </s>
  <s xml:id="echoid-s1115" xml:space="preserve">Fig. </s>
  <s xml:id="echoid-s1116" xml:space="preserve">16. </s>
  <s xml:id="echoid-s1117" xml:space="preserve">Cylindrus AD <lb/>diam. </s>
  <s xml:id="echoid-s1118" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1119" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1120" xml:space="preserve">ſuſtinet alas, 60 p. </s>
  <s xml:id="echoid-s1121" xml:space="preserve">longas, quae antea deſcri-
<pb o="51" file="0061" n="61" rhead="DE MOLIS ALATIS HYDRAVLICIS."/>
ptarum cetera ſimiles ſunt. </s>
  <s xml:id="echoid-s1122" xml:space="preserve">Eidem affixa eſt rota FE, <lb/>diam. </s>
  <s xml:id="echoid-s1123" xml:space="preserve">8 {1/2} p. </s>
  <s xml:id="echoid-s1124" xml:space="preserve">clauis 44 inſtructa, quibus mouet tympa-<lb/>num H, diam. </s>
  <s xml:id="echoid-s1125" xml:space="preserve">6 p. </s>
  <s xml:id="echoid-s1126" xml:space="preserve">fuſos habet 28, alt. </s>
  <s xml:id="echoid-s1127" xml:space="preserve">18 dig. </s>
  <s xml:id="echoid-s1128" xml:space="preserve">Hoc <lb/>tympanum rotat axem ligneum l, diam. </s>
  <s xml:id="echoid-s1129" xml:space="preserve">1 p. </s>
  <s xml:id="echoid-s1130" xml:space="preserve">altit. </s>
  <s xml:id="echoid-s1131" xml:space="preserve">22 p. <lb/></s>
  <s xml:id="echoid-s1132" xml:space="preserve">qui intra quatuor columnas, quibus mola nititur, con-<lb/>ſiſtit. </s>
  <s xml:id="echoid-s1133" xml:space="preserve">infra ferreus axis inſertus eſt, craſſus 8 dig. </s>
  <s xml:id="echoid-s1134" xml:space="preserve">bra-<lb/>chium KL prominet 18 dig. </s>
  <s xml:id="echoid-s1135" xml:space="preserve">et LM 8 dig. </s>
  <s xml:id="echoid-s1136" xml:space="preserve">cui in extre-<lb/>mo cupreus annulus ſiue modiolus additur. </s>
  <s xml:id="echoid-s1137" xml:space="preserve">huic co-<lb/>pulantur uncis brachia TM, MN, XM, MP, ex <lb/>quibus duo 5 p. </s>
  <s xml:id="echoid-s1138" xml:space="preserve">tertium 4 {3/4} p. </s>
  <s xml:id="echoid-s1139" xml:space="preserve">quartum 5 {1/4} p. </s>
  <s xml:id="echoid-s1140" xml:space="preserve">longitu-<lb/>dinem habent. </s>
  <s xml:id="echoid-s1141" xml:space="preserve">Altera parte haec brachia appre-<lb/>hendunt normas quatuor N, P, T, X, quarum ca-<lb/>thetus eſt 7 p. </s>
  <s xml:id="echoid-s1142" xml:space="preserve">baſis 8 p. </s>
  <s xml:id="echoid-s1143" xml:space="preserve">firmantur tum uinculis <lb/>ligneis, ut figura docet, tum ferreis, inter extrema <lb/>extenſis. </s>
  <s xml:id="echoid-s1144" xml:space="preserve">baſis incumbit trabibus, et beneficio axis <lb/>ferrei intra caua aenea ſiti moueri poteſt. </s>
  <s xml:id="echoid-s1145" xml:space="preserve">Nimi-<lb/>rum, quando cum axe ligneo imum manubrium <lb/>curuatum torquetur, attrahuntur ab una parte nor-<lb/>marum extrema T et X, et propelluntur oppoſita <lb/>N, P, ſunt autem baſibus annexa ferra craſſa 1 {1/4} dig. </s>
  <s xml:id="echoid-s1146" xml:space="preserve"><lb/>longa 15 p. </s>
  <s xml:id="echoid-s1147" xml:space="preserve">quae embolos inuerſos gerunt, et hi <lb/>aſcendendo et deſcendendo, protrudunt uel hauri-<lb/>unt aquam, quam per alias fiſtulas amplius aſcen-<lb/>dere cogunt, plane, uti cap. </s>
  <s xml:id="echoid-s1148" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1149" xml:space="preserve">et 2. </s>
  <s xml:id="echoid-s1150" xml:space="preserve">uberrime eſt <lb/>explicatum. </s>
  <s xml:id="echoid-s1151" xml:space="preserve">fiſtula f@@rea, in qua mouetur embo-<lb/>lus, alta eſt 4 p. </s>
  <s xml:id="echoid-s1152" xml:space="preserve">diam. </s>
  <s xml:id="echoid-s1153" xml:space="preserve">6 dig. </s>
  <s xml:id="echoid-s1154" xml:space="preserve">motus emboli in <lb/>eadem fit in perpendiculo 18 digitorum. </s>
  <s xml:id="echoid-s1155" xml:space="preserve">Aquae <lb/>ex quatuor fiſtulis, tandem in unicam diam. </s>
  <s xml:id="echoid-s1156" xml:space="preserve">10 dig. </s>
  <s xml:id="echoid-s1157" xml:space="preserve"><lb/>propelluntur, quae eas ad receptaculum euehit. </s>
  <s xml:id="echoid-s1158" xml:space="preserve"><lb/>aqua in puteum per aquaeductum deriuata plerum-<lb/>que habet profunditatem 10 p. </s>
  <s xml:id="echoid-s1159" xml:space="preserve">Altitudo muri ſu-<lb/>pra horizontem eſt 18 p. </s>
  <s xml:id="echoid-s1160" xml:space="preserve">his ſi addas 22 p. </s>
  <s xml:id="echoid-s1161" xml:space="preserve">altitudi-<lb/>nem axis medii, producitur altitudo moletrinae 40 p.</s>
  <s xml:id="echoid-s1162" xml:space="preserve">
<pb o="52" file="0062" n="62" rhead="CAP. III. DE MOLIS ALATIS HYDRAVL."/>
a ſolo usque ad axem tympani. </s>
  <s xml:id="echoid-s1163" xml:space="preserve">murus praeterea 8 p. <lb/></s>
  <s xml:id="echoid-s1164" xml:space="preserve">infra horizontem altera parte continuatur, in quo <lb/>porta facta eſt, per quam in puteum et ad fiſtulas <lb/>uia patet. </s>
  <s xml:id="echoid-s1165" xml:space="preserve">Quae de freno dixi ſupra, hic quoque ua-<lb/>lent. </s>
  <s xml:id="echoid-s1166" xml:space="preserve">ad uenti flatum diriguntur molae ope axis cum <lb/>peritrochio, quae palis circa molas poſitis annecti et <lb/>firmari ſolet.</s>
  <s xml:id="echoid-s1167" xml:space="preserve"/>
</p>
<div xml:id="echoid-div17" type="float" level="2" n="4">
<note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">Fig. XVI. <lb/>Tab. IV.</note>
</div>
<p>
  <s xml:id="echoid-s1168" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1169" xml:space="preserve">Tametſi autem haec moletrina non tantam at-<lb/>tollit aquarum molem quantam altera, tamen a moli-<lb/>tore priori praeferebatur, ob ſoliditatem, et quia mo-<lb/>tus aequabilior eſt. </s>
  <s xml:id="echoid-s1170" xml:space="preserve">Agitatur etiam uentis imbecillio-<lb/>ribus, et uelis tantum paucis opus habet, quod facilita-<lb/>tem motus comprobat. </s>
  <s xml:id="echoid-s1171" xml:space="preserve">Copia aquarum ex ſuperiori-<lb/>bus aeſtimari poteſt. </s>
  <s xml:id="echoid-s1172" xml:space="preserve">Ducuntur autem omnes in <lb/>hortum arci adiacentem, ut ibidem in ſublime ſa-<lb/>liant.</s>
  <s xml:id="echoid-s1173" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1174" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1175" xml:space="preserve">Illud hic ſilentio non inuoluendum eſt, quod <lb/>PETRVS. </s>
  <s xml:id="echoid-s1176" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1177" xml:space="preserve">nuper defunctus Ruſſorum Imperator. </s>
  <s xml:id="echoid-s1178" xml:space="preserve">glor. <lb/></s>
  <s xml:id="echoid-s1179" xml:space="preserve">mem. </s>
  <s xml:id="echoid-s1180" xml:space="preserve">cum has molas hydraulicas uento mouendas <lb/>praefens contemplaretur, tam magni earum ingenio-<lb/>ſam ſtructuram fecerit, ut Ipſe ſingularum partium <lb/>menſuras capere, et in ſuos pugillares referre non <lb/>dubitauerit.</s>
  <s xml:id="echoid-s1181" xml:space="preserve"/>
</p>
<pb o="53" file="0063" n="63"/>
</div>
<div xml:id="echoid-div19" type="section" level="1" n="11">
<head xml:id="echoid-head24" xml:space="preserve">CAPVT IV. <lb/>DE <lb/>MACHINA HYDRAVLICA <lb/>LONDINENSI <lb/>IN QVA <lb/>VIS IGNIS AQVAS IN VAPORES <lb/>RESOLVENTIS, CONSPICVA EST.</head>
<head xml:id="echoid-head25" xml:space="preserve">3<unsure/>.</head>
<p>
  <s xml:id="echoid-s1182" xml:space="preserve">Ignem quoque ad machinas hydraulicas motu in-<lb/>ſtruendas ualere, ſatis hodie indubiis experimen-<lb/>tis conſtat. </s>
  <s xml:id="echoid-s1183" xml:space="preserve">Inprimis hoc confirmat, machina <lb/>Britannica, tum conformationis elegantia, tum <lb/>ſucceſſu admirabilis. </s>
  <s xml:id="echoid-s1184" xml:space="preserve">primum tentamen a Thoma Savery <lb/>Anglo factum et oblatum eſt Societati Reg. </s>
  <s xml:id="echoid-s1185" xml:space="preserve">Scient. <lb/></s>
  <s xml:id="echoid-s1186" xml:space="preserve">Londini a. </s>
  <s xml:id="echoid-s1187" xml:space="preserve">1699. </s>
  <s xml:id="echoid-s1188" xml:space="preserve">m. </s>
  <s xml:id="echoid-s1189" xml:space="preserve">lun. </s>
  <s xml:id="echoid-s1190" xml:space="preserve">v. </s>
  <s xml:id="echoid-s1191" xml:space="preserve">Tranſact. </s>
  <s xml:id="echoid-s1192" xml:space="preserve">Angl. </s>
  <s xml:id="echoid-s1193" xml:space="preserve">ann. </s>
  <s xml:id="echoid-s1194" xml:space="preserve">ei. </s>
  <s xml:id="echoid-s1195" xml:space="preserve">n. </s>
  <s xml:id="echoid-s1196" xml:space="preserve"><lb/>253. </s>
  <s xml:id="echoid-s1197" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1198" xml:space="preserve">228. </s>
  <s xml:id="echoid-s1199" xml:space="preserve">et <emph style="sc">Lovvthorp</emph> Epitome Tom. </s>
  <s xml:id="echoid-s1200" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1201" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1202" xml:space="preserve">544. </s>
  <s xml:id="echoid-s1203" xml:space="preserve"><lb/>deſcriptum in libello, cui titulus, The miners friend, ſ. </s>
  <s xml:id="echoid-s1204" xml:space="preserve"><lb/>foſſoris metallorum amicus. </s>
  <s xml:id="echoid-s1205" xml:space="preserve">quem hactenus mihi uidere <lb/>non licuit. </s>
  <s xml:id="echoid-s1206" xml:space="preserve">ex eodem repetiit praecipua momenta I <emph style="sc">O</emph>-<lb/><emph style="sc">ANNES</emph> <emph style="sc">Harris</emph> in Lexico technico anglice edito, <lb/>uoce Engine. </s>
  <s xml:id="echoid-s1207" xml:space="preserve">ſubiit tamen hoc inuentum ex eo tempo-<lb/>re uarias mutationes, donec abhinc annis octo conſe-<lb/>queretur eam, qua hodie Londini, ea in regione quae <lb/>Yorck Building nominatur, in ripa Tameſis, unde ad <lb/>altitudinem 124 pedum angl. </s>
  <s xml:id="echoid-s1208" xml:space="preserve">aquas attollit, et in prae-<lb/>cipuas ampliſſimae urbis domos diffundit, cernitur. </s>
  <s xml:id="echoid-s1209" xml:space="preserve"><lb/>Siquidem noctu nunc diuque laborem ſine ullo pericu-<lb/>
<pb o="54" file="0064" n="64" rhead="CAPVT IV."/>
lo continuat, et ſemetipſam moderatur. </s>
  <s xml:id="echoid-s1210" xml:space="preserve">Hanc for-<lb/>
<anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/>
mam, prouti Londini nuper perſpicua imagine reprae-<lb/>ſentata et explicata eſt, proferam Figura 17, una cum <lb/>interpretatione obſeruationum anglicarum picturae ad-<lb/>ditarum, et cogitationibus quibusdam ſingularibus, <lb/>quae ad eiusdem machinae ſtructuram plenius intelli-<lb/>gendam ſpectant.</s>
  <s xml:id="echoid-s1211" xml:space="preserve"/>
</p>
<div xml:id="echoid-div19" type="float" level="2" n="1">
<note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">Fig. XVII. <lb/>Tab. 3. &amp; <lb/>Fig. XVIII. <lb/>Tab. 4.</note>
</div>
<p style="it">
  <s xml:id="echoid-s1212" xml:space="preserve">A Deſcription of the Engine for raiſing vvater by Fire.</s>
  <s xml:id="echoid-s1213" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1214" xml:space="preserve">A The Fire place.</s>
  <s xml:id="echoid-s1215" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1216" xml:space="preserve">B.</s>
  <s xml:id="echoid-s1217" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1218" xml:space="preserve">large Boiler or alembic, three parts full of wa-<lb/>ter, the Steam wereof is confined by a cloſe ſpherical <lb/>Top, and kept of a due uniform force.</s>
  <s xml:id="echoid-s1219" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1220" xml:space="preserve">C. </s>
  <s xml:id="echoid-s1221" xml:space="preserve">A Braſſ cylinder, woſe diameter is more or leſſ, <lb/>according to the Depth and Quantity of water, to be <lb/>drawn in ſuch proportion, that the Preſſure of <lb/>the atmoſphere upon the area of its baſe may over-<lb/>poiſe and raiſe the pillar of water with a proper ve-<lb/>locity.</s>
  <s xml:id="echoid-s1222" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1223" xml:space="preserve">D. </s>
  <s xml:id="echoid-s1224" xml:space="preserve">The Pipe thro which the Steam paſſes from the <lb/>Boiler into the cylinder.</s>
  <s xml:id="echoid-s1225" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1226" xml:space="preserve">E. </s>
  <s xml:id="echoid-s1227" xml:space="preserve">The axis of the regulator, that opens and ſhuts <lb/>that End of the Pipe D, within the Boiler, wich re-<lb/>gulates the whole motion of the Engine, by permit-<lb/>ting the Steam, to aſcend and puſh up, or ſuffer the <lb/>Piſton to riſe, and confining the Steam when riſen, <lb/>in order to its condenſation, by an injection of cold <lb/>water, which making a Vacuum there, the pi-<lb/>ſton is immediately depreſſed by the Wight of the <lb/>atmoſphere.</s>
  <s xml:id="echoid-s1228" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1229" xml:space="preserve">F. </s>
  <s xml:id="echoid-s1230" xml:space="preserve">A loaded Value, which giues Vent to the Steam <lb/>of the Boiler, in caſe it grows to ſtrong.</s>
  <s xml:id="echoid-s1231" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1232" xml:space="preserve">G. </s>
  <s xml:id="echoid-s1233" xml:space="preserve">Two Gage Cocks with their Pipes, on of <lb/>which goes down, ſo far into the Boiler, as to be, 2
<pb o="55" file="0065" n="65" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
or 3 Inches above, and the other, ſo far below the <lb/>ſurface of the water therein, when it is of a due <lb/>height; </s>
  <s xml:id="echoid-s1234" xml:space="preserve">theſe are, to find the exceſſ or defect of wa-<lb/>ter in the Boiler, it being of a due height, when ſte-<lb/>am is emitted by the ſhorter, and water by the <lb/>longeſt Pipe.</s>
  <s xml:id="echoid-s1235" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1236" xml:space="preserve">H. </s>
  <s xml:id="echoid-s1237" xml:space="preserve">A Pipe fix'd to the Head of the Boiler, and <lb/>called the Buoy-Pipe, open at both Ends, the lower <lb/>End being a foot or more below the ſurface of the <lb/>water, in the Boiler, in which is a cylindrical Buoy, <lb/>that ſwims upon the water therein, and when the <lb/>Steam in the Boiler is become ſo ſtrong, as by its <lb/>Preſſure to force the water up into the ſaid Pipe, it <lb/>then raiſes the Buoy, whoſe Shanck 12 cauſes the Bal-<lb/>lance R and Inceptor 7, alſo to riſe, and lifting <lb/>the notch 2 from 3 on the End of the Leaver oo<unsure/>, <lb/>Permits No. </s>
  <s xml:id="echoid-s1238" xml:space="preserve">13 a wight hanging thereto, to fall ſo far, <lb/>till thereby the injecting Cock at N (the axis of the <lb/>ſaid Leaver) is opened, by which a Injection of cold <lb/>water being made, and conſequently a vacuum (by <lb/>the condenſation of the Steam procured) the preſſure <lb/>of the atmoſphere on the Piſton brings down b (the <lb/>inner end of the great Leaver) when on of the three <lb/>Pins in the hanging Beam Q, that comes down with <lb/>the great Leaver, takes hold of n. </s>
  <s xml:id="echoid-s1239" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1240" xml:space="preserve">one End of the <lb/>Leaver oo, which by the fall of the wigt. </s>
  <s xml:id="echoid-s1241" xml:space="preserve">13 at the <lb/>other End, was raiſed, as above, ſomewhat heigher <lb/>than the Parallel of its axis at N, and brings it down <lb/>ſo far till the End 3 is raiſed up high enough to be <lb/>again taken hold of by the notch 2, at which Time the <lb/>injecting-Cock is thereby ſhut, and the Regulator E <lb/>opened, as deſcribed under the letter Q.</s>
  <s xml:id="echoid-s1242" xml:space="preserve"/>
</p>
<pb o="56" file="0066" n="66" rhead="CAPVT IV."/>
<p>
  <s xml:id="echoid-s1243" xml:space="preserve">IK. </s>
  <s xml:id="echoid-s1244" xml:space="preserve">A Pipe and Cock whereby the Boiler is ſup-<lb/>plied with warm Water from the Top of the cy-<lb/>linder.</s>
  <s xml:id="echoid-s1245" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1246" xml:space="preserve">L. </s>
  <s xml:id="echoid-s1247" xml:space="preserve">The Shanck of the Piſton, whoſe lower Part is a <lb/>circular Plate, in diameter near equal to the Cylin-<lb/>der, and cloſeth thereto with the Leather round the <lb/>Edge having always 6 or 8 Inches of water upon it, to <lb/>prevent the atmoſphere from getting down, and <lb/>when the Steam is let into the cylinder, which takes <lb/>of or contrevails the Preſſure on the Piſton, it roſes <lb/>with the inner End of the great Leaver b, by a Coun-<lb/>treballance an the other End b. </s>
  <s xml:id="echoid-s1248" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1249" xml:space="preserve">and when a Va-<lb/>cuum is made, it deſcends by the weight of the atmo-<lb/>ſphere, and brings down the End of the Leaver b <lb/>with a Power capable of raiſing at the other End b 2 <lb/>any weight, not exceeding the Preſſure of the at-<lb/>moſphere on a Cylinder of the diameter made <lb/>uſe of.</s>
  <s xml:id="echoid-s1250" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1251" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1252" xml:space="preserve">The Injecting-Pipe bringing down cold water <lb/>from the ciſtern, g.</s>
  <s xml:id="echoid-s1253" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1254" xml:space="preserve">N. </s>
  <s xml:id="echoid-s1255" xml:space="preserve">The Injecting Cock with its Wheel, which is <lb/>oppend and ſhut by</s>
</p>
<p>
  <s xml:id="echoid-s1256" xml:space="preserve">OOA ſmal Leaver, and its quarter Wheel, whoſe <lb/>two Ends n. </s>
  <s xml:id="echoid-s1257" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1258" xml:space="preserve">et 3 are alternatly liftet up by the Engi-<lb/>nes motion.</s>
  <s xml:id="echoid-s1259" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1260" xml:space="preserve">P. </s>
  <s xml:id="echoid-s1261" xml:space="preserve">An axis moving between two Standards with <lb/>its Shanks no. </s>
  <s xml:id="echoid-s1262" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1263" xml:space="preserve">5. </s>
  <s xml:id="echoid-s1264" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1265" xml:space="preserve">8. </s>
  <s xml:id="echoid-s1266" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1267" xml:space="preserve">and a Slider no. </s>
  <s xml:id="echoid-s1268" xml:space="preserve">10, fix'd to <lb/>the Spanner, or handle of the regulator, for opening <lb/>and ſhutting it.</s>
  <s xml:id="echoid-s1269" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1270" xml:space="preserve">Q. </s>
  <s xml:id="echoid-s1271" xml:space="preserve">A Beam hanging on the great Leaver, and mo-<lb/>ving with it up and down perpendicularly, which <lb/>opens and ſhuts the regulator and Injecting-Cock, by <lb/>means of 3 Pins, ſet higher or lower, as occaſion re-
<pb o="57" file="0067" n="67" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
quires, one of which as the Beam is going up (upon the <lb/>acceſſ of the Steam into the cylinder) takes hold of <lb/>the Shank No. </s>
  <s xml:id="echoid-s1272" xml:space="preserve">8. </s>
  <s xml:id="echoid-s1273" xml:space="preserve">belonging to the Axis P, and raiſes <lb/>it to ſuch a height, till the Weight 14, on the top of <lb/>the ſhank no. </s>
  <s xml:id="echoid-s1274" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1275" xml:space="preserve">gets beyond the perpendicular of the <lb/>Axis, when, by its own Gravity it falls ſo far towards <lb/>the Cylinder, as the Piece of Leather no. </s>
  <s xml:id="echoid-s1276" xml:space="preserve">15. </s>
  <s xml:id="echoid-s1277" xml:space="preserve">will per-<lb/>mitt it, by which motion the Shank 5, (the End of <lb/>which appears in the Draught, at a Pin in the Slider <lb/>no. </s>
  <s xml:id="echoid-s1278" xml:space="preserve">10.) </s>
  <s xml:id="echoid-s1279" xml:space="preserve">is removed, and the ſhank 4 brought down, <lb/>to take its Place, and ſtriking againſt the ſaid Pin car-<lb/>ries it away ſo far, and with it the Slider, till the Re-<lb/>gulator at E, to whoſe Handle the ſaid Slider is faſti-<lb/>ned, is thereby ſhut, and the Steam confined in the <lb/>Boiler, and by the ſame motion the ſhank no. </s>
  <s xml:id="echoid-s1280" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1281" xml:space="preserve">(which <lb/>in the Draught appears ſhutting downward) is raiſed <lb/>ſomewhat above the parallel of the Axis P, and lies <lb/>ready to be taken hold of by an other Pin in the han-<lb/>ging Beam Q, which upon the condenſation of the <lb/>Steam, (as deſcribed under the letter H) brings down <lb/>this Shank ſo far, till the Weight 14 is againſt brought <lb/>beyond the Perpendicular of the Axis P, on the other <lb/>ſide, when by its own gravity the ſaid Weight falls ſo <lb/>far from the cylinder, as the Piece of Leather 16 will <lb/>permitt; </s>
  <s xml:id="echoid-s1282" xml:space="preserve">by which M@tion, the ſhank 4 is again remo-<lb/>ved from the aboveſa@@ Pin in the Slider, and the <lb/>ſhank 5 brought to ſtrike againſt it, whereby the Re-<lb/>gulator is opend, at which Time the Steam having a <lb/>free Paſſage out of the Boiler into the Cylinder, and <lb/>the Preſſure upon the ſurface of the Water in the Boi-<lb/>ler being abated, the Buoy in the Pipe H falls, and with it <lb/>the Ballance R, and Inceptor 7, and the Notch 2 taking <lb/>hold of the End 3, of the Leaver oo whereby the In-
<pb o="58" file="0068" n="68" rhead="CAPVT IV."/>
jecting-Cock remains ſhut, after the Pin in the Beam <lb/>Q, (in riſing) leaves the End 1, of that Leaver, by <lb/>which it was before ſhut, as deſcribed under the Let-<lb/>ter H, at the ſame Time alſo the Steam having free <lb/>acceſſ from the Boiler into the Cylinder, by its force <lb/>againſt the bottom of the Piſton countervails the Preſ-<lb/>ſure of the Atmoſphere, and permits it to riſe with b, <lb/>the inner End of the great Leaver, with alſo riſes the <lb/>hanging Beam Q, and by the Pin firſt mentioned ſhuts <lb/>the Regulator. </s>
  <s xml:id="echoid-s1283" xml:space="preserve">when the Steam being confined and <lb/>the Injecting-Cock ſhut, the Engine remains in this <lb/>Poſture until the Steam becomes ſtrong enough <lb/>by its Preſſure on the Water in the Boiler to raiſe the <lb/>Buoy in the Pipe Hand a new ſtroke by condenſation <lb/>is begun; </s>
  <s xml:id="echoid-s1284" xml:space="preserve">but if the Steam be ſtrong enough, as it moſt <lb/>uſually happens, then, as ſoon as the Piſton is come <lb/>to its proper height, a new Strocke is immediately be-<lb/>gun, and the Engine almoſt in continual Motion, ma-<lb/>king from 12 to 16, and ſometimes 20 Strockes, in a <lb/>minute, whilſt b 2 the outer End of the great Leaver, <lb/>works a Pump of 8, 9 or 12 Inches diameter, and giues <lb/>a Strock of 7 foot or more in Length.</s>
  <s xml:id="echoid-s1285" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1286" xml:space="preserve">R. </s>
  <s xml:id="echoid-s1287" xml:space="preserve">A Ballance, one End of which turns upen a Pin, <lb/>and the other faſtend to the higher End of the Ince-<lb/>ptor 7, to the lower End of which is faſtened the <lb/>Ballance 11, that hath the N@@’ch 2 under it; </s>
  <s xml:id="echoid-s1288" xml:space="preserve">theſe riſe <lb/>and fall all together, by means of the Buoy in H, and <lb/>ſerve to open the Injecting-Cock N, as deſcribed un-<lb/>der the letter H; </s>
  <s xml:id="echoid-s1289" xml:space="preserve">and alſo to keep the ſaid Cock ſ hut, <lb/>when the Pin in the Beam Q on its riſing leaves <lb/>the End 1 of the Leaver oo, as deſeribed under the <lb/>Letter Q.</s>
  <s xml:id="echoid-s1290" xml:space="preserve"/>
</p>
<pb o="59" file="0069" n="69" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
<p>
  <s xml:id="echoid-s1291" xml:space="preserve">S. </s>
  <s xml:id="echoid-s1292" xml:space="preserve">A Cup receiving the overplus Water from x, <lb/>which conveys it into the Boiler.</s>
  <s xml:id="echoid-s1293" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1294" xml:space="preserve">T. </s>
  <s xml:id="echoid-s1295" xml:space="preserve">The Pipe carrying down the injected Water <lb/>from the Cylinder, thro a immerged valve at y.</s>
  <s xml:id="echoid-s1296" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1297" xml:space="preserve">V. </s>
  <s xml:id="echoid-s1298" xml:space="preserve">A Pipe carrying the waſte water from the Piſton, <lb/>when it riſes to the top of the Cylinder.</s>
  <s xml:id="echoid-s1299" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1300" xml:space="preserve">W A Pipe ſupplying the valve with Water from <lb/>the top of the Piſton.</s>
  <s xml:id="echoid-s1301" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1302" xml:space="preserve">X. </s>
  <s xml:id="echoid-s1303" xml:space="preserve">A Value thro which the Steam forces out the <lb/>Air, that paſſes into the Cylinder with the injected <lb/>Water.</s>
  <s xml:id="echoid-s1304" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1305" xml:space="preserve">Y. </s>
  <s xml:id="echoid-s1306" xml:space="preserve">A Value letting out the injected Water, which <lb/>being immerged in a Ciſtern of Water, prevents the <lb/>Air from going up into the Cylinder thro it, when a <lb/>Vacuum is made therein.</s>
  <s xml:id="echoid-s1307" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1308" xml:space="preserve">Z. </s>
  <s xml:id="echoid-s1309" xml:space="preserve">A Cock ſupplying the Piſton with Water from <lb/>the Ciſtern, g.</s>
  <s xml:id="echoid-s1310" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1311" xml:space="preserve">aaaa. </s>
  <s xml:id="echoid-s1312" xml:space="preserve">Four great Beams ſupporting the Engine and <lb/>the Floor of the Houſe.</s>
  <s xml:id="echoid-s1313" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1314" xml:space="preserve">bcde The Ground Floor of the Houfe.</s>
  <s xml:id="echoid-s1315" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1316" xml:space="preserve">f The Chimney.</s>
  <s xml:id="echoid-s1317" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1318" xml:space="preserve">g A ciſtern of cold Water to ſupply the Injecting-<lb/>Pipe.</s>
  <s xml:id="echoid-s1319" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1320" xml:space="preserve">b1. </s>
  <s xml:id="echoid-s1321" xml:space="preserve">b2 The Great Leaver, moving on an Axis in the <lb/>middle, to the inner @nd of which the ſhank of the <lb/>Piſton is faſtned by a C@ain, that hangs down from <lb/>the Arch.</s>
  <s xml:id="echoid-s1322" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1323" xml:space="preserve">i. </s>
  <s xml:id="echoid-s1324" xml:space="preserve">A Rod and Chain fixed to the outer End of the <lb/>great Leaver. </s>
  <s xml:id="echoid-s1325" xml:space="preserve">working Pumps from the Bottom of <lb/>the mine.</s>
  <s xml:id="echoid-s1326" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1327" xml:space="preserve">k. </s>
  <s xml:id="echoid-s1328" xml:space="preserve">A ſmal pump ſupplying the Ciſtern g, thro the <lb/>Pipe m, m.</s>
  <s xml:id="echoid-s1329" xml:space="preserve"/>
</p>
<pb o="60" file="0070" n="70" rhead="CAPVT IV."/>
<p>
  <s xml:id="echoid-s1330" xml:space="preserve">l. </s>
  <s xml:id="echoid-s1331" xml:space="preserve">A Windleſſ, Axis, and Rope, whereby men and <lb/>materials are conveyed up and down the mine.</s>
  <s xml:id="echoid-s1332" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1333" xml:space="preserve">m, m. </s>
  <s xml:id="echoid-s1334" xml:space="preserve">A Pipe which by the little Pump k ſupplies <lb/>the Ciſtern g with Water.</s>
  <s xml:id="echoid-s1335" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1336" xml:space="preserve">ppp the ground Floor before the Fireplace.</s>
  <s xml:id="echoid-s1337" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1338" xml:space="preserve">q. </s>
  <s xml:id="echoid-s1339" xml:space="preserve">Steps going down to the fire place.</s>
  <s xml:id="echoid-s1340" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1341" xml:space="preserve">r. </s>
  <s xml:id="echoid-s1342" xml:space="preserve">A Pipe conveying the waſte Water from the <lb/>Ciſtern g.</s>
  <s xml:id="echoid-s1343" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div21" type="section" level="1" n="12">
<head xml:id="echoid-head26" style="it" xml:space="preserve">Interpretatio latina earundem obſerua-<lb/>tionum.</head>
<p>
  <s xml:id="echoid-s1344" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1345" xml:space="preserve">Fornax.</s>
  <s xml:id="echoid-s1346" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1347" xml:space="preserve">B. </s>
  <s xml:id="echoid-s1348" xml:space="preserve">Ahenum magnum, cuius duae partes tertiae a-<lb/>quis repletae ſunt, in quo uapor concluditur operculo <lb/>ſphaerico, ut conſimilem ſemper extenſionem con-<lb/>ſeruet.</s>
  <s xml:id="echoid-s1349" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1350" xml:space="preserve">C. </s>
  <s xml:id="echoid-s1351" xml:space="preserve">Cylindrus aeneus, cuius diameter amplior con-<lb/>tractiorque eſt, pro ratione profunditatis et copiae a-<lb/>quarum extollendarum, ita ut preſſus aeris columnam <lb/>aqueam uelocitate debita propellat.</s>
  <s xml:id="echoid-s1352" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1353" xml:space="preserve">D. </s>
  <s xml:id="echoid-s1354" xml:space="preserve">Fiſtula per quam uapor ex aheno cylindrum C <lb/>ingreditur.</s>
  <s xml:id="echoid-s1355" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1356" xml:space="preserve">E. </s>
  <s xml:id="echoid-s1357" xml:space="preserve">Axis rectoris, ſiue epiſtomii, quod aperit et oc-<lb/>cludit os fiſtulae D intra ahenum. </s>
  <s xml:id="echoid-s1358" xml:space="preserve">Quo ipſo mode-<lb/>ratur motum totius machinae@@um efficit, ut exhalatio <lb/>aquae diffundat ſeſe, et embolus in cylindro C aſcen-<lb/>dit; </s>
  <s xml:id="echoid-s1359" xml:space="preserve">iterumque cohibito uapore, permittit, ut iniectu <lb/>aquae frigidae uapor ſubito condenſatus Vacuum ſpa-<lb/>tium producat, ut embolus aeris pondere oneratus, <lb/>celerrime delabatur.</s>
  <s xml:id="echoid-s1360" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1361" xml:space="preserve">F. </s>
  <s xml:id="echoid-s1362" xml:space="preserve">Valuula plumbea, quaepatitur, ut uapor ex ahe-<lb/>no erumpat, quando ibidem abundat.</s>
  <s xml:id="echoid-s1363" xml:space="preserve"/>
</p>
<pb o="61" file="0071" n="71" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
<p>
  <s xml:id="echoid-s1364" xml:space="preserve">G. </s>
  <s xml:id="echoid-s1365" xml:space="preserve">Duo epiſtomia exploratoria, cum fiſtulis annexis, <lb/>quarum altera in ahenum porrigitur 2 uel 3 digitis, al-<lb/>tera in aquam ipſam tantundem penetrat, cum ea ha-<lb/>bet debitam in lebete profunditatem. </s>
  <s xml:id="echoid-s1366" xml:space="preserve">Itaque haec epi-<lb/>ſtomia ſeruiunt ad explorandum defectum et exces-<lb/>ſum aquarum in uaporario. </s>
  <s xml:id="echoid-s1367" xml:space="preserve">Nimirum aquae copia <lb/>ſufficiens ineſt, cum aperto epiftomio per breuiorem <lb/>fiſtulam uapor, et per longiorem aqua prorumpit.</s>
  <s xml:id="echoid-s1368" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1369" xml:space="preserve">H. </s>
  <s xml:id="echoid-s1370" xml:space="preserve">Fiſtula in ſummo aheni collocata, dicitur fulci-<lb/>ens, cuius patet os externum et internum. </s>
  <s xml:id="echoid-s1371" xml:space="preserve">Hoc intra <lb/>aquas longitudine pedis unius et amplius merſum eſt. <lb/></s>
  <s xml:id="echoid-s1372" xml:space="preserve">Intra fiſtulam autem natat ſuper aquis lignum teres <lb/>trunco copulatum; </s>
  <s xml:id="echoid-s1373" xml:space="preserve">et cum uapor in aheno uiolentior <lb/>redditur, aqua aſſurgit in laudata fiſtula, lignum inna-<lb/>tans una aſcendit, et truncus eius 12 eodem tempore <lb/>tollit regulam R (Anglus nominat libramentum, Bal-<lb/>lance, quia ſurſum deorſumque libratur) et regulam ſiue <lb/>columellam perpendicularem 7 quae inceptor uocatur; </s>
  <s xml:id="echoid-s1374" xml:space="preserve"><lb/>tum recedit inciſura 2, ab extremo 3, parui uectis oo, <lb/>cuius pondus 13, ſubito deorſum ruit, et quia idem ue-<lb/>ctis affixus eſt epiſtomio iniectionis N, efficit, ut hoc <lb/>uertatur, et per foramen ſic patens aqua frigida, ex re-<lb/>ceptaculog per tubum M delapla, ſeſe inſinuet, quae, <lb/>quia per perpendiculum 12. </s>
  <s xml:id="echoid-s1375" xml:space="preserve">pedum deſcendit, in cylin-<lb/>dro C in altum proſilit, et fonticulum producit. </s>
  <s xml:id="echoid-s1376" xml:space="preserve">Hinc, <lb/>condenſatione uaporun facta, uacuum oritur, et pres-<lb/>ſus atmoſphaerae embolo incumbentis deprimit extre-<lb/>mum tigni librantis interius b; </s>
  <s xml:id="echoid-s1377" xml:space="preserve">ſimul deſcendit etiam <lb/>tignum perpendiculare Q (quod in medio cauum, et <lb/>utrimque aliqua foramina, quibus tres claui teretes <lb/>ferrei inſeruntur, habet) et unus ex clauis quos ge-<lb/>rit, apprehendit extremum uectis parui oo, (quod an-<lb/>tea deſcenſu ponderis 13 ſurſum ultra axem ſuum N,
<pb o="62" file="0072" n="72" rhead="CAPVT IV."/>
conuerſum erat, ut ante dictum fuit.) </s>
  <s xml:id="echoid-s1378" xml:space="preserve">idemque tan-<lb/>tum deprimit, donec extremum 3 ſatis elatum eſt, ut <lb/>iterum in crenam ſiue inciſuram 2 reuertatur, quo ipſo <lb/>epiſtomium iniectionis clauditur, et rectoris epiſtomi-<lb/>um aperitur, quemadmodum ſub litera Q explica-<lb/>bitur.</s>
  <s xml:id="echoid-s1379" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1380" xml:space="preserve">IK. </s>
  <s xml:id="echoid-s1381" xml:space="preserve">fiſtula cum epiſtomio, per quam in ahenum aqua <lb/>calida ex cylindro deriuatur.</s>
  <s xml:id="echoid-s1382" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1383" xml:space="preserve">L. </s>
  <s xml:id="echoid-s1384" xml:space="preserve">Embolus, cuius pars ima eſt lamina circularis, <lb/>diametrum cauo cylindri reſpondentem habens, ueſti-<lb/>tusque undique corio. </s>
  <s xml:id="echoid-s1385" xml:space="preserve">ſuper quem ſemper aqua 6 uel 8 <lb/>digitos alta affunditur, ne aer intra cylindrum deſuper <lb/>penetret. </s>
  <s xml:id="echoid-s1386" xml:space="preserve">Quando autem uapor in cylindrum ſurgit, <lb/>uincit preſſionem ponderis aerei, et brachium tigni li-<lb/>brantis b attollitur, a pondere brachii b 2; </s>
  <s xml:id="echoid-s1387" xml:space="preserve">et dum ite-<lb/>rum uacuum exoritur, deſcendit b, et adducitur b 2, <lb/>uirtute tali, quae preſſui uel ponderi aeris ſuper embo-<lb/>lo cylindri magni iacentis, aequipollet.</s>
  <s xml:id="echoid-s1388" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1389" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1390" xml:space="preserve">Fiſtula iniectionis, deducens aquas ex ciſter-<lb/>na g.</s>
  <s xml:id="echoid-s1391" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1392" xml:space="preserve">N. </s>
  <s xml:id="echoid-s1393" xml:space="preserve">Epiſtomium iniectionis cum rota dentata, aperit <lb/>idem et claudit</s>
</p>
<p>
  <s xml:id="echoid-s1394" xml:space="preserve">OO paruus uectis, cui additus eſt quadransrotae den-<lb/>tatae, dum nempe uectis extrema 1 et 3 motu machinae <lb/>alternatim deprimuntur et attolluntur.</s>
  <s xml:id="echoid-s1395" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1396" xml:space="preserve">P. </s>
  <s xml:id="echoid-s1397" xml:space="preserve">Axis uolubilis intra du@@ columellas, cum radiis <lb/>ſiue anſis ſuis No. </s>
  <s xml:id="echoid-s1398" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1399" xml:space="preserve">5. </s>
  <s xml:id="echoid-s1400" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1401" xml:space="preserve">8. </s>
  <s xml:id="echoid-s1402" xml:space="preserve">9, et curſore no. </s>
  <s xml:id="echoid-s1403" xml:space="preserve">10, affixo an-<lb/>ſae rectoris (quae nihil aliud eſt, quam ferrum ſesqui-<lb/>pedale foramina habens, in quae pro copulando cur-<lb/>ſore claui inſeruntur.) </s>
  <s xml:id="echoid-s1404" xml:space="preserve">pro eodem aperiendo et clau-<lb/>dendo.</s>
  <s xml:id="echoid-s1405" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1406" xml:space="preserve">Q, Tïgnum penſile, affixum magno libratori, et <lb/>cum hoc ſurſum deorſumque agitatum, aperiens et
<pb o="63" file="0073" n="73" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
claudens rectorem, et epiſtomium iniectionis, beneficio tri-<lb/>um clauorum, altius humiliusque, uti neceſſitas requi-<lb/>rit, poſitorum. </s>
  <s xml:id="echoid-s1407" xml:space="preserve">Vnus nempe ex iis, cum aſcendit ti-<lb/>gnum, (penetrante in cylindrum uapore) apprehendit <lb/>brachium No. </s>
  <s xml:id="echoid-s1408" xml:space="preserve">8, et idem tantum tollit, donec pondus <lb/>14, in extremo brachii 9, reflectit ultra perpendicula-<lb/>rem axis, dum proprio pondere tantum uerſus cylin-<lb/>drum accedit, quantum corrigiae 15 longitudo patitur, <lb/>quo motu oppoſitum brachium 5, (cuius extremum in <lb/>figura clauo curſoris No. </s>
  <s xml:id="echoid-s1409" xml:space="preserve">10 imminet) recedit, et ſe-<lb/>quens brachium 4 in eius locum ſufficitur, quod ſtrin-<lb/>gens clauum curſoris, eum et curſorem eousque pro-<lb/>trudit, donec rector E, cuius anſa curſori affixa, clau-<lb/>datur, et uapor in aheno coerceatur. </s>
  <s xml:id="echoid-s1410" xml:space="preserve">Eodem motu <lb/>brachium No. </s>
  <s xml:id="echoid-s1411" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1412" xml:space="preserve">aſſurgit paululum ſupra lineam axi P. <lb/></s>
  <s xml:id="echoid-s1413" xml:space="preserve">parallelam, et eum ſitum aſſequitur, ut ab altero clauo <lb/>tigni penſilis, v. </s>
  <s xml:id="echoid-s1414" xml:space="preserve">lit. </s>
  <s xml:id="echoid-s1415" xml:space="preserve">H. </s>
  <s xml:id="echoid-s1416" xml:space="preserve">tantum detrudatur, donec pon-<lb/>dus 14, iterum ultra axis P perpendiculum in alteram <lb/>partem reflexum eſt, dum nempe pondere ſiue grauitate <lb/>ſua tantum recedit a cylindro C, quantum permittit <lb/>corrigia 16. </s>
  <s xml:id="echoid-s1417" xml:space="preserve">hinc brachium 4 denuo a curſore remoue-<lb/>tur, et ſequens 5 ſuccedit, ut ſtringendo clauum curſo-<lb/>ris rector aperiatur, et uapor liberum in cylindrum ac-<lb/>ceſſum conſequatur. </s>
  <s xml:id="echoid-s1418" xml:space="preserve">Tum ceſſante preſſione uaporum <lb/>in aquas lebetis, lignum fiſtulae H decidit, et cum eo <lb/>regula librans R, et In@@ptor 7. </s>
  <s xml:id="echoid-s1419" xml:space="preserve">inciſura autem 2 recipit <lb/>extremum 3, uectis oo, ſic epiſtomium iniectionis <lb/>clauſum manet, poſtea clauus tigni Q aſcendentis, <lb/>mittit extremum 1, ut dictum ſub lit. </s>
  <s xml:id="echoid-s1420" xml:space="preserve">H. </s>
  <s xml:id="echoid-s1421" xml:space="preserve">Itaque uapor <lb/>ingreſſus cylindrum attollens embolum et tignum Q, <lb/>clauo antea dicto rector clauditur. </s>
  <s xml:id="echoid-s1422" xml:space="preserve">et uapore coercito, <lb/>et epiſtomio iniectionis occluſo, hoc ſitu machina re-<lb/>linquitur, donec exhalationum uis iterum tollat li-
<pb o="64" file="0074" n="74" rhead="CAPVT IV."/>
gnum natans in fiſtula H, et nouus motus, ſacta uaporum <lb/>condenſatione, producatur. </s>
  <s xml:id="echoid-s1423" xml:space="preserve">Quandoquidem tamen, <lb/>et utplurimum, exhalatio ſatis ualida eſt, ut motus <lb/>continuus efficiatur, et intra minutum temporis 12, 16 <lb/>et quandoque 20. </s>
  <s xml:id="echoid-s1424" xml:space="preserve">pulſus contingant, quibus ſemper h 2. <lb/></s>
  <s xml:id="echoid-s1425" xml:space="preserve">alterum et externum extremum librilis magni, agitat <lb/>antliam cuius diameter 8, 9, 12 pollicum eſt, et mo-<lb/>tus emboli in antlia intra perpendiculum 7 pedum <lb/>continetur.</s>
  <s xml:id="echoid-s1426" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1427" xml:space="preserve">R. </s>
  <s xml:id="echoid-s1428" xml:space="preserve">Regula, quae libramentum paruum nominatur, <lb/>cuius finiſtrum extremum ſuper clauo quieſcit, et de-<lb/>xtrum cum inceptore 7 copulatur, huius inferiori par-<lb/>ti adhaeret regula altera 11, habens infra inciſuram 2. <lb/></s>
  <s xml:id="echoid-s1429" xml:space="preserve">hae duae regulae cum perpendiculo inceptoris, ſur-<lb/>gunt et cadunt ſimul, prout motus ligni in H natan-<lb/>tis, cum trunco ſuo iubet, et ſeruiunt aperiendo et <lb/>claudendo epiſtomio iniectionis N. </s>
  <s xml:id="echoid-s1430" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s1431" xml:space="preserve">lit. </s>
  <s xml:id="echoid-s1432" xml:space="preserve">H. </s>
  <s xml:id="echoid-s1433" xml:space="preserve">et Q.</s>
  <s xml:id="echoid-s1434" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1435" xml:space="preserve">S. </s>
  <s xml:id="echoid-s1436" xml:space="preserve">Patella quae redundantem in altera X aquam <lb/>recipit et in ahenum deducit.</s>
  <s xml:id="echoid-s1437" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1438" xml:space="preserve">T. </s>
  <s xml:id="echoid-s1439" xml:space="preserve">Fiſtula deducens a cylindro aquas iniectas, per <lb/>fiſtulam, cuius ualuula in uas Y aqua plenum im-<lb/>merſa eſt.</s>
  <s xml:id="echoid-s1440" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1441" xml:space="preserve">V. </s>
  <s xml:id="echoid-s1442" xml:space="preserve">Fiſtula deducens ſuperfluas ab embolo aquas, <lb/>quando ſummum cylindri attingit.</s>
  <s xml:id="echoid-s1443" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1444" xml:space="preserve">W. </s>
  <s xml:id="echoid-s1445" xml:space="preserve">Fiſtula, quae aquam ſuper ualuulam X ducit, <lb/>epiſtomio in fine munita,</s>
</p>
<p>
  <s xml:id="echoid-s1446" xml:space="preserve">X. </s>
  <s xml:id="echoid-s1447" xml:space="preserve">Valuula per quam uapor eiicit ex cylindro ae-<lb/>rem, qui cum aqua iniecta in eundem ſeſe inſinuauit.</s>
  <s xml:id="echoid-s1448" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1449" xml:space="preserve">Y. </s>
  <s xml:id="echoid-s1450" xml:space="preserve">Valuula uiam faciens aquae in cylindrum inie-<lb/>ctae, et impediens aerem, ne in eum aſſurgat, quando <lb/>ibi uacuum condenſatione ſpatium producitur.</s>
  <s xml:id="echoid-s1451" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1452" xml:space="preserve">Z. </s>
  <s xml:id="echoid-s1453" xml:space="preserve">Epiſtomium permittens, ut aquae ex ciſterna g <lb/>in embolum illabatur.</s>
  <s xml:id="echoid-s1454" xml:space="preserve"/>
</p>
<pb o="65" file="0075" n="75" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
<p>
  <s xml:id="echoid-s1455" xml:space="preserve">a a. </s>
  <s xml:id="echoid-s1456" xml:space="preserve">Trabes, tum machinam, tum aedium impoſi-<lb/>tarum contignationem, ſuſtinentes.</s>
  <s xml:id="echoid-s1457" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1458" xml:space="preserve">b. </s>
  <s xml:id="echoid-s1459" xml:space="preserve">c. </s>
  <s xml:id="echoid-s1460" xml:space="preserve">d. </s>
  <s xml:id="echoid-s1461" xml:space="preserve">e. </s>
  <s xml:id="echoid-s1462" xml:space="preserve">ſolum aediſicii.</s>
  <s xml:id="echoid-s1463" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1464" xml:space="preserve">f. </s>
  <s xml:id="echoid-s1465" xml:space="preserve">fumarium.</s>
  <s xml:id="echoid-s1466" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1467" xml:space="preserve">g. </s>
  <s xml:id="echoid-s1468" xml:space="preserve">Ciſterna aquae frigidae plena, pro fiſtula inie-<lb/>ctionis.</s>
  <s xml:id="echoid-s1469" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1470" xml:space="preserve">h. </s>
  <s xml:id="echoid-s1471" xml:space="preserve">h2. </s>
  <s xml:id="echoid-s1472" xml:space="preserve">Magnum librile, circa axem in medio mobi-<lb/>le, cuius extremo interiori arcuato ex catena embolus <lb/>cum trunco ſuo pendulus adhaeret.</s>
  <s xml:id="echoid-s1473" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1474" xml:space="preserve">i. </s>
  <s xml:id="echoid-s1475" xml:space="preserve">Truncus et catena, adhaerens exteriori librilis ex-<lb/>tremo, et antlias in puteo uel fodina poſitas in motum <lb/>ciens.</s>
  <s xml:id="echoid-s1476" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1477" xml:space="preserve">k. </s>
  <s xml:id="echoid-s1478" xml:space="preserve">Exiguae antliae truncus embolum gerens, pro <lb/>ducenda per fiſtulam m aqua in ciſternam g.</s>
  <s xml:id="echoid-s1479" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1480" xml:space="preserve">l. </s>
  <s xml:id="echoid-s1481" xml:space="preserve">Axis cum peritrochio, et funiculo, quo homines <lb/>et materiae in puteum demittuntur.</s>
  <s xml:id="echoid-s1482" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1483" xml:space="preserve">m. </s>
  <s xml:id="echoid-s1484" xml:space="preserve">Fiſtula, per quam antlia k ducit aquas in ciſter-<lb/>nam g.</s>
  <s xml:id="echoid-s1485" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1486" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1487" xml:space="preserve">ſolum ante fornacem.</s>
  <s xml:id="echoid-s1488" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1489" xml:space="preserve">q. </s>
  <s xml:id="echoid-s1490" xml:space="preserve">gradus, per quos ad fornacem deſcenditur.</s>
  <s xml:id="echoid-s1491" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1492" xml:space="preserve">r. </s>
  <s xml:id="echoid-s1493" xml:space="preserve">Fiſtula aquas ſuperfluas ex ciſterna g abducens.</s>
  <s xml:id="echoid-s1494" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1495" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1496" xml:space="preserve">Quamuis Figura 17 totius machinae et partium <lb/>eius ſitum ob oculos poſuerim, tamen cum ob exigui-<lb/>tatem picturae, quorundam exiliorum membrorum re-<lb/>praeſentatio obſcurior r@@dita ſit, hinc adieci figurae <lb/>maioris, qualis a <emph style="sc">Svttone</emph> <emph style="sc">Nichols</emph> a. </s>
  <s xml:id="echoid-s1497" xml:space="preserve">1725 deli-<lb/>neata et ſculpta, apud <emph style="sc">Ioannem</emph> <emph style="sc">King</emph> Londini uen-<lb/>ditur, diſtinctiorem delineationem, Fig. </s>
  <s xml:id="echoid-s1498" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1499" xml:space="preserve">Tab. </s>
  <s xml:id="echoid-s1500" xml:space="preserve">IV. <lb/></s>
  <s xml:id="echoid-s1501" xml:space="preserve">ex qua tum fabricam operis, tum menſuras partium <lb/>pleniſſime perſpici poſſe, exiſtimo. </s>
  <s xml:id="echoid-s1502" xml:space="preserve">Operae autem <lb/>
<anchor type="note" xlink:label="note-0075-01a" xlink:href="note-0075-01"/>
pretium eſt notaſſe, quod modus, per alternas uices <lb/>aperiendi et claudendi epiſtomia E et N. </s>
  <s xml:id="echoid-s1503" xml:space="preserve">adeoque ad-
<pb o="66" file="0076" n="76" rhead="CAPVT IV."/>
mittendi in cylindrum Cuaporem uel aquam frigidam, <lb/>qualis ſupra traditus eſt, uariari queat, ita, ut fiſtula ſul-<lb/>cri et ligno natante H in eadem machina careat. </s>
  <s xml:id="echoid-s1504" xml:space="preserve">Nam <lb/>pro epiſtomio E ſufficiunt duo ferra recurua, affixa co-<lb/>lumellae, ante tignum penſile Q erectae, quae motu <lb/>huius tigni attrahunt curſorem et repellunt. </s>
  <s xml:id="echoid-s1505" xml:space="preserve">Et capiti <lb/>epiſtomii N, ſi tranſuerſum ferrum imponatur, et aliud <lb/>duobus brachiis inſtructum, et axi uectis O O additum, <lb/>in trabe a a infigatur, ſimiliter alternis aſcenſibus et de-<lb/>ſcenſibus perpendiculi Q, idem epiſtomium aperietur <lb/>et claudetur, motusque adeo ſolo laudato perpendicu-<lb/>lo continuabitur. </s>
  <s xml:id="echoid-s1506" xml:space="preserve">Quod executi ſunt Angli quidam, <lb/>qui machinam ſimilem prope Lutetiam Pariſiorum, in <lb/>uilla Paſſy, conſtruxerunt, et eius effectus Academiae <lb/>ſcientiarum Regiae demonſtrarunt.</s>
  <s xml:id="echoid-s1507" xml:space="preserve"/>
</p>
<div xml:id="echoid-div21" type="float" level="2" n="1">
<note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">Tab. IV. <lb/>Fig. 18.</note>
</div>
<p>
  <s xml:id="echoid-s1508" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1509" xml:space="preserve">Similiter multo ſimpliciorem opportunioremque <lb/>huius machinae compoſitionem reddidit celeberrimus <lb/><emph style="sc">Dn</emph>. </s>
  <s xml:id="echoid-s1510" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1511" xml:space="preserve">T. </s>
  <s xml:id="echoid-s1512" xml:space="preserve"><emph style="sc">Desagviliers</emph>, qualem an. </s>
  <s xml:id="echoid-s1513" xml:space="preserve">1726. </s>
  <s xml:id="echoid-s1514" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1515" xml:space="preserve">Au-<lb/>guſto Londiniin area aedium eiusdem, iuxta ripam Tha-<lb/>meſis ripam ſitarum, non ſine uoluptate ſum contempla-<lb/>tus. </s>
  <s xml:id="echoid-s1516" xml:space="preserve">Scilicet laudati uiri auſpiciis, ſumtibus ſocietatis <lb/>cuiusdam parata erat machina moduli minoris, eum in <lb/>finem, ut eodem adhuc anno Toletum in Carpetanis <lb/>transmitteretur, ibidemque ſimilis formae amplioris <lb/>erigeretur, quae Tagi aquas attolleret, et in ciuium To-<lb/>letanorum domos, alto in co<gap/> aedificatas, deriuaret: <lb/></s>
  <s xml:id="echoid-s1517" xml:space="preserve">Ex cuius operis fabrica lucrum inſigne, priuilegio Re-<lb/>gis Hiſpaniarum decretum, Angli illi ſocii ſperabant. </s>
  <s xml:id="echoid-s1518" xml:space="preserve"><lb/>In hoc exemplo machinae affabre facto, arcus ferreus <lb/>bifurcus, circa axem duabus columellis inſertum uolu-<lb/>bilis, a tigno penſili Q, clauos geſtante, ſurſum deor-<lb/>ſum que agitatus curſorem 10 modo adducebat modo <lb/>repellebat, atque inſimul ualuulam rectoris E per uices
<pb o="67" file="0077" n="77" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
aperiebat uel occludebat. </s>
  <s xml:id="echoid-s1519" xml:space="preserve">Sed quia motu tigni penſilis <lb/>etiam regitur uectis O. </s>
  <s xml:id="echoid-s1520" xml:space="preserve">O, ut hic facilius officium ſuum <lb/>faciat, loco quadrantis, quem ante data deſcriptio re-<lb/>quirit, ferrum bifurcum circa clauum uerſatile aſſumi-<lb/>tur, quod prorſum retrorſumque mouetur, et epiſto-<lb/>mium N ferro tranſuerſo praeditum per uices aperit <lb/>et claudit. </s>
  <s xml:id="echoid-s1521" xml:space="preserve">Niſi fallor memoria, eadem emendatio <lb/>iamiam ann. </s>
  <s xml:id="echoid-s1522" xml:space="preserve">1726. </s>
  <s xml:id="echoid-s1523" xml:space="preserve">adhibita ſpectabatur machinae ma-<lb/>iori, quae Londini ad ripam Thameſis proſperrimo <lb/>ſucceſſu incredibilem aquarum uim in motum ciet. </s>
  <s xml:id="echoid-s1524" xml:space="preserve">In <lb/>Paſſiacenſi machina idem artificium obuium habui, <lb/>cuius adhuc in ſcriniis meis aſſeruo accuratam perſpi-<lb/>cuamque delineationem Pariſiis mecum communica-<lb/>tam. </s>
  <s xml:id="echoid-s1525" xml:space="preserve">Praeterea in exemplo illo machinae minori ant-<lb/>liam aliter deprehendi conformatam. </s>
  <s xml:id="echoid-s1526" xml:space="preserve">Erat illa ſecun-<lb/>di generis aſpirans et premens, de qua dixi Cap. </s>
  <s xml:id="echoid-s1527" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1528" xml:space="preserve">§. <lb/></s>
  <s xml:id="echoid-s1529" xml:space="preserve">VIII. </s>
  <s xml:id="echoid-s1530" xml:space="preserve">nempe adducto intra cylindrum embolo, aquae <lb/>ex puteo ſupra ualuulam aſſurgebant, deinde embolo <lb/>retruſo, in aliam fiſtulam ualuula itidem praeditam pro-<lb/>pellebantur, et ad inſignem altitudinem eleuabantur. </s>
  <s xml:id="echoid-s1531" xml:space="preserve"><lb/>Verum ut aquarum expulſio in altum fiat, requiritur <lb/>ſtabile ferrum loco catenae, quo, dum a uapore eleua-<lb/>tur embolus L, alter i ex librante tigno h 2 ſuſpenſus <lb/>deorſum ualide protrudatur, ut ſuperando aqueae co-<lb/>lumnae altioris oneri parem uirtutem conſequeretur. </s>
  <s xml:id="echoid-s1532" xml:space="preserve"><lb/>Quantum autem robur @uaporis expanſione proficiſci <lb/>queat, utique experientiae duntaxat documento com-<lb/>probandum eſt.</s>
  <s xml:id="echoid-s1533" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1534" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1535" xml:space="preserve">Menſuras operis ex ſcala addita petere licet. </s>
  <s xml:id="echoid-s1536" xml:space="preserve">An-<lb/>glicae deſcriptionis auctor eam omiſit, quare eam ſup-<lb/>pleui, machinarum, quae Londini et in uilla Paſſy ere-<lb/>ctae ſunt, attentiore contemplatione. </s>
  <s xml:id="echoid-s1537" xml:space="preserve">Diameter cy-<lb/>lindri maioris eſt 2 {1/2} p. </s>
  <s xml:id="echoid-s1538" xml:space="preserve">altitudo 9 p. </s>
  <s xml:id="echoid-s1539" xml:space="preserve">ahenum latum 8
<pb o="68" file="0078" n="78" rhead="CAPVT IV."/>
uel 9 p. </s>
  <s xml:id="echoid-s1540" xml:space="preserve">cuius formam ellipticam Paſſiaci notaui, al-<lb/>tum 6 p. </s>
  <s xml:id="echoid-s1541" xml:space="preserve">ibidem ferreus eſt cylindrus C, ſed Londini ae-<lb/>reus lamina lebetis craſſa {1/6} digit. </s>
  <s xml:id="echoid-s1542" xml:space="preserve">cylindri paries craſſus <lb/>{1/2} dig.</s>
  <s xml:id="echoid-s1543" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1544" xml:space="preserve">5. </s>
  <s xml:id="echoid-s1545" xml:space="preserve">Deſcriptio ſuperior tantum machinam exhibet, <lb/>tanquam ſuper fodinam ad aquas exhauriendas poſi-<lb/>tam, et antliae aſpiranti mouendae deſtinatam. </s>
  <s xml:id="echoid-s1546" xml:space="preserve">Sic <lb/>autem non niſi ad mediocrem altitudinem aquas ele-<lb/>uari palam eſt. </s>
  <s xml:id="echoid-s1547" xml:space="preserve">Quamobrem peruellem ut tentare-<lb/>tur applicatio embolorum inuerſorum prementium, <lb/>quia ad altiorem aquae columnam ſuſtinendam et at-<lb/>tollendam, pondus atmoſphaerae embolo L incumbens <lb/>ſatis uirium ſubminiſtrat. </s>
  <s xml:id="echoid-s1548" xml:space="preserve">Vapor enim hic nihil mo-<lb/>uet, praeter embolum LL, de quo inferius plura. </s>
  <s xml:id="echoid-s1549" xml:space="preserve">de-<lb/>turbatio eiusdem preſſu aeris atmoſphaerici fit, ue-<lb/>rum emboli ex h<unsure/> 2 pendentes, cum deſcendunt, ab <lb/>embolo L non truduntur, ſed proprio pondere de-<lb/>mitti debent. </s>
  <s xml:id="echoid-s1550" xml:space="preserve">quare tales eligendi, quorum deſcenſus <lb/>quam minime impediatur. </s>
  <s xml:id="echoid-s1551" xml:space="preserve">In antlia aſpirante deſcen-<lb/>f<unsure/>urus embolus eam habeat grauitatem, ut uincat at-<lb/>tritum, et in aquam ſub eo praecedente aſcenſu et ſuctu <lb/>collectam mergatur. </s>
  <s xml:id="echoid-s1552" xml:space="preserve">et quia attritus emboli intra poli-<lb/>tam cylindri ſuperficiem perpendiculariter commoti, <lb/>non nimis uehemens eſt, conſequitur inde, pondus <lb/>ferrorum, ex quibus emboli pendent, ſufficere poſſe, <lb/>ad eos demittendos, et coria <gap/>aluularum ſurſum con-<lb/>uertenda, ut in aquam mergantur, praeſertim cum <lb/>emboli coriis elatis laxius in fiſtulis pendeant. </s>
  <s xml:id="echoid-s1553" xml:space="preserve">Et <lb/>tales emboli cernuntur in machina Paſſiacenſi. </s>
  <s xml:id="echoid-s1554" xml:space="preserve">Sed <lb/>his ipſis aquas effundi debere in receptaculum, quod <lb/>ponitur intra perpendiculum, in quo truncus emboli <lb/>agitatur, palam eſt.</s>
  <s xml:id="echoid-s1555" xml:space="preserve"/>
</p>
<pb o="69" file="0079" n="79" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
<p>
  <s xml:id="echoid-s1556" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1557" xml:space="preserve">Hinc probatu facile erit, quod emboli premen-<lb/>tes inuerſi, aſpirantibus multum praeſtent. </s>
  <s xml:id="echoid-s1558" xml:space="preserve">Quoad <lb/>deſcenſum enim ſimiles ſunt aſpirantium, et nihil am-<lb/>plius requiritur, quam,@ ut uincant attritum cylindri, <lb/>et ſurſum conuertant ualuulas coriaceas, quod modo <lb/>ante explicato obtinetur. </s>
  <s xml:id="echoid-s1559" xml:space="preserve">Quoad aſcenſum autem <lb/>quam maxime differunt. </s>
  <s xml:id="echoid-s1560" xml:space="preserve">Nam aquam ſupra ſe admiſ-<lb/>ſam, non pro ratione perpendiculi, in quo mouentur, <lb/>attollunt, ſed dum uis ſufficiat, per fiſtulas alias ad in-<lb/>ſignem amplius altitudinem ueluti eiaculantur. </s>
  <s xml:id="echoid-s1561" xml:space="preserve">Quod <lb/>ſi inſuper facultas motrix patiatur, poſſunt una ſub ſe <lb/>adducere embolos aſpirantes, quos cap. </s>
  <s xml:id="echoid-s1562" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1563" xml:space="preserve">§. </s>
  <s xml:id="echoid-s1564" xml:space="preserve">4. </s>
  <s xml:id="echoid-s1565" xml:space="preserve">luculen-<lb/>tius deſcripſi, quo ipſo denuo augent altitudinem mo-<lb/>tus aquarum ex imo puteo eductarum. </s>
  <s xml:id="echoid-s1566" xml:space="preserve">et tum demum <lb/>foſſoribus ſalutaris eſt eiusmodi machina, qui quanto <lb/>profundius in terram penetrant, tanto maiorem aqua-<lb/>rum ſubterranearum copiam reperiunt.</s>
  <s xml:id="echoid-s1567" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1568" xml:space="preserve">7. </s>
  <s xml:id="echoid-s1569" xml:space="preserve">Vt igitur de proportione uirtutis neceſſariae <lb/>rectius iudicium feratur, ſequentia obſeruaſſe iuuaue-<lb/>rit. </s>
  <s xml:id="echoid-s1570" xml:space="preserve">Duplex nimirum uis mouens in hac machina <lb/>occurrit. </s>
  <s xml:id="echoid-s1571" xml:space="preserve">altera uaporis, ſiue exhalationum, pro em-<lb/>bolo in ſublime leuando, altera ponderis aerei, pro <lb/>eodem reducendo, et tollendo ſimul pondere, quod ex <lb/>extremo tigni h 2 pendet. </s>
  <s xml:id="echoid-s1572" xml:space="preserve">Exhalationum diſtentio <lb/>uincere debet, tum pondus emboli, tum tigni Q Q. <lb/></s>
  <s xml:id="echoid-s1573" xml:space="preserve">non licuit mihi accura@e metiri brachia librilis h, h 2, <lb/>fi tamen picturae fides habenda eſt, digitis circiter <lb/>ſex externum h 2 longius eſt interno h, eſt itaque hoc <lb/>ponderoſius, et praeterea embolis et eorum longuriis <lb/>oneratum, uideturque exceſſus eius tantus eſſe, ut <lb/>emboli L grauitatem et attritum materiae, et partem <lb/>etiam aerei ponderis compenſet, hinc uapor reliquum <lb/>aeris niſuro ſuperare debet, cuius tamen aeſtimatio <lb/>uix melius, quam ex mirandis, quos ante memora-
<pb o="70" file="0080" n="80" rhead="CAPVT IV."/>
ui, effectibus intelligi poteſt. </s>
  <s xml:id="echoid-s1574" xml:space="preserve">Interim de aliorum <lb/>periculis hic diſſerere non uidetur ab inſtituto alie-<lb/>num. </s>
  <s xml:id="echoid-s1575" xml:space="preserve">Scilicet uim et expanſionem longe maximam <lb/>aquae in uapores calore reſolutae iampridem ueteres <lb/>perſpectam habuere, prouti docet <emph style="sc">Vitrvvivs</emph> <lb/>Architecturae Lib. </s>
  <s xml:id="echoid-s1576" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1577" xml:space="preserve">cap. </s>
  <s xml:id="echoid-s1578" xml:space="preserve">VI. </s>
  <s xml:id="echoid-s1579" xml:space="preserve">qui paruulo aeolipilae <lb/>ſpectaculo de immanibus uentorum naturae rationi-<lb/>bus iudicari poſſe cenſuit. </s>
  <s xml:id="echoid-s1580" xml:space="preserve">Verum quo modo pote-<lb/>ſtas uaporum uehementer expanſorum definienda ſit, <lb/>ſolertius poſteri indagarunt. </s>
  <s xml:id="echoid-s1581" xml:space="preserve">Primus forte idem ten-<lb/>tauit eximius philoſophiae experimentalis promotor <lb/><emph style="sc">Franciscvs</emph> <emph style="sc">Baco de</emph> <emph style="sc">Vervlamio</emph>, is enim de-<lb/>ſcribit hiſtoriam expanſionis materiae in pneumaticis <lb/>ut loquitur in libro, cui titulum fecit, impetus philoſo-<lb/>phici, col. </s>
  <s xml:id="echoid-s1582" xml:space="preserve">705. </s>
  <s xml:id="echoid-s1583" xml:space="preserve">operum. </s>
  <s xml:id="echoid-s1584" xml:space="preserve">Sumſit phialam uitream, quae <lb/>fortaſſe unciam unam capiebat, cuius collum labro la-<lb/>tiore reuerſo erat inſtructum, eamque dimidiam aqua <lb/>repleuit, et pondus eius et aquae contentae bilance <lb/>expendit, dein ueſicam, quae circiter pintam continebat, <lb/>recentem, oleoque bene obturatam, ad os phialae fi-<lb/>lo cerato fortiter alligauit, et phialam ſuper carbo-<lb/>nes candentes collocauit; </s>
  <s xml:id="echoid-s1585" xml:space="preserve">aqua non ita multo poſt <lb/>bullire coepit, et paulatim ueſicam ex omni parte <lb/>ſufflauit, fereque ad rupturam extendit, quod cum <lb/>fieret, ſtatim uitrum ab igne remotum et ſuper tape-<lb/>tem poſitum fuit, ne repent@@o frigore disrumpere-<lb/>tur; </s>
  <s xml:id="echoid-s1586" xml:space="preserve">tum in ſummo ueſicae acu foramen aperuit, per <lb/>quod uapor ſubito erumpebat. </s>
  <s xml:id="echoid-s1587" xml:space="preserve">poſtea ueſicam prorſus <lb/>a phiala remouit, et eius iterum pondus quaeſiuit, <lb/>reperitque duorum denariorum pondus aquam amiſis-<lb/>ſe inde collegit, uaporem, qui ueſicam implebat, denari-<lb/>orum duorum ponderiaequipollere, ipſumque uaporem <lb/>aquae ad corpus aquae rationem octogecuplam habuiſ-
<pb o="71" file="0081" n="81" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
ſe. </s>
  <s xml:id="echoid-s1588" xml:space="preserve">At quia in hoc experimento, dimidia parte aere <lb/>repletam phialam adhibuit, minime eſt dubitandum, <lb/>huius expanſionem uaporum aeſtimationem pertur-<lb/>baſſe. </s>
  <s xml:id="echoid-s1589" xml:space="preserve">Interim augmentum uoluminis uaporum a <lb/>Bacone proditum magnum nimis haud eſſe, recentio-<lb/>rum phyſicorum experimenta comprobarunt. </s>
  <s xml:id="echoid-s1590" xml:space="preserve">Soler-<lb/>tiſſimi ſodales academiae Florentinae, quae del cimento, <lb/>ab honeſto uirtutis et ingenii certamine appellatur, <lb/>qui ſub Leopoldi Ducis Hetruriae auſpiciis, ſuperiore <lb/>ſeculo naturalis ſcientiae incrementa promouere an-<lb/>niſi ſunt, cum inueſtigarent, utrum aqua compreſſa, <lb/>in anguſtius ſpatium redigi poſſit, eum in finem duas <lb/>ſphaeras, primum uitreas, deinceps cupreas, diuerſae <lb/>magnitudinis, tubis uitreis inſtructas, adhibuerunt, <lb/>hasque repleuerunt aqua, ita ut haec ultra ſphaeras in <lb/>tubulis ſubſiſteret, tum utriusque tubi uitrei ora, liqua-<lb/>to uitro ſic copularunt, ut aquae et aeri in tubis hae-<lb/>renti, liber ex uno tubo in alterum progreſſus relin-<lb/>queretur, ipſae autem ſphaerae obliqua tubulorum <lb/>coniunctione longius pauliſper a ſeinuicem ſeiunge-<lb/>bantur. </s>
  <s xml:id="echoid-s1591" xml:space="preserve">Quo facto, ambabus ſphaeris applicata ſunt <lb/>duo pocula glaciei contritae plena, ita ut glacies totas <lb/>ſphaeras ambiret, et aqua incluſa ad ſummum conden-<lb/>ſationis gradum reduceretur, iamque relictus in angulo <lb/>coniunctionis exiguus tubulus uitreus, adhuc apertus, <lb/>hermetice claudebatur. </s>
  <s xml:id="echoid-s1592" xml:space="preserve">@ Simulac clauſus omnino erat <lb/>tubus, ſphaera maior ex glacie eximebatur, primumque <lb/>in aquam tepidam, poſtea etiam in ebullientem immit-<lb/>tebatur, ut aqua intus contenta calore uehementiſſime <lb/>expanderetur, aſcendebat haec ultra extremum tubuli, <lb/>qui ſphaerae maiori adhaerebat, et in alterum conne-<lb/>xum aſſurgebat, interim aqua alterius ſphaerae mino-<lb/>ris, glacie undique cinctae, ſtatum maximae condenſa-
<pb o="72" file="0082" n="82" rhead="CAPVT IV."/>
tionis ſeruabat, tum curioſe obſeruatores annotabant, <lb/>utrum haec aqua, cylindri aerei imminentis, fortiter a <lb/>uapore protruſi, preſſioni cederet, et nonnihil uerſus <lb/>ſphaeram ſuam comprimeretur, ſed id minime accidit, <lb/>potius ſphaerae uitreae in glacie poſitae ſundum dif-<lb/>fregit, et quando cuprea adhibebatur, aqua per metalli <lb/>ferrumen tranſiit, manifeſto uirium prementium indi-<lb/>cio. </s>
  <s xml:id="echoid-s1593" xml:space="preserve">Ex hoc et ſimilibus experimentis didicere Flo-<lb/>rentini, quod uis, quae aerem in ſpatium trigeſies mi-<lb/>nus, quam ante occupabat, reducit, non potuerit, ne <lb/>ad capilli latitudinem, comprimere molem aquae, <lb/>quamuis forte centies et millies maior eſſet. </s>
  <s xml:id="echoid-s1594" xml:space="preserve">Et licet <lb/>laudati huius experimenti auctores proportionis alla-<lb/>tae demonſtrationem haud dederint, ſuppleuit tamen <lb/>eandem, totumque experimentum copioſius illuſtra-<lb/>uit, celeberrimus tentaminum Florentinorum editor <lb/><emph style="sc">Dn</emph>. </s>
  <s xml:id="echoid-s1595" xml:space="preserve">P<emph style="sc">ET. VAN</emph> <emph style="sc">Mvsschenbroek</emph>, p. </s>
  <s xml:id="echoid-s1596" xml:space="preserve">60. </s>
  <s xml:id="echoid-s1597" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s1598" xml:space="preserve">Poſt <lb/>Florentinos uaporum uim incredibilem nouo experi-<lb/>mento ob oculos poſuit <emph style="sc">Dion</emph>. </s>
  <s xml:id="echoid-s1599" xml:space="preserve"><emph style="sc">Papinvs</emph>, coquo uel <lb/>digeſtore, quem nominat, ſuo, cuius quia nota eſt com-<lb/>poſitio, de eodem amplius hic dicere ſuperuacaneum <lb/>eſſe arbitror. </s>
  <s xml:id="echoid-s1600" xml:space="preserve">deſcribitur uberius in Tr. </s>
  <s xml:id="echoid-s1601" xml:space="preserve">Gall. </s>
  <s xml:id="echoid-s1602" xml:space="preserve">La ma-<lb/>niere d amolir les os et de faire cuire toute ſorte de viande <lb/>en fort peu de tems, par Mr. </s>
  <s xml:id="echoid-s1603" xml:space="preserve">Papin. </s>
  <s xml:id="echoid-s1604" xml:space="preserve">Amſtelod. </s>
  <s xml:id="echoid-s1605" xml:space="preserve">1688. </s>
  <s xml:id="echoid-s1606" xml:space="preserve">conf. <lb/></s>
  <s xml:id="echoid-s1607" xml:space="preserve">Acta Eruditor. </s>
  <s xml:id="echoid-s1608" xml:space="preserve">Lipſ. </s>
  <s xml:id="echoid-s1609" xml:space="preserve">a. </s>
  <s xml:id="echoid-s1610" xml:space="preserve">1682. </s>
  <s xml:id="echoid-s1611" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1612" xml:space="preserve">105. </s>
  <s xml:id="echoid-s1613" xml:space="preserve">305. </s>
  <s xml:id="echoid-s1614" xml:space="preserve">a. </s>
  <s xml:id="echoid-s1615" xml:space="preserve">1687. </s>
  <s xml:id="echoid-s1616" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1617" xml:space="preserve">276. </s>
  <s xml:id="echoid-s1618" xml:space="preserve">et <lb/><emph style="sc">Io</emph><unsure/>. </s>
  <s xml:id="echoid-s1619" xml:space="preserve"><emph style="sc">Chr</emph>. </s>
  <s xml:id="echoid-s1620" xml:space="preserve"><emph style="sc">Stvrmii</emph> phyſica@@lectiua Tom. </s>
  <s xml:id="echoid-s1621" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1622" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1623" xml:space="preserve">539. </s>
  <s xml:id="echoid-s1624" xml:space="preserve"><lb/>Comparari etiam merentur, quae de motu rarefactio-<lb/>nis, experimentis comprobato, congeſſit <emph style="sc">Franci</emph>-<lb/><emph style="sc">SCVS</emph> <emph style="sc">Tertivs de</emph> <emph style="sc">Lanis</emph>, magiſterii naturae et <lb/>artis Tomo II. </s>
  <s xml:id="echoid-s1625" xml:space="preserve">Lib. </s>
  <s xml:id="echoid-s1626" xml:space="preserve">VIII. </s>
  <s xml:id="echoid-s1627" xml:space="preserve">cap. </s>
  <s xml:id="echoid-s1628" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1629" xml:space="preserve">num. </s>
  <s xml:id="echoid-s1630" xml:space="preserve">55. </s>
  <s xml:id="echoid-s1631" xml:space="preserve">74.</s>
  <s xml:id="echoid-s1632" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1633" xml:space="preserve">8. </s>
  <s xml:id="echoid-s1634" xml:space="preserve">Reſtat, ut in pondus aeris inquiramus. </s>
  <s xml:id="echoid-s1635" xml:space="preserve">Inno-<lb/>teſcit idem generatim ex aequilibrio columnae aqueae <lb/>uel argenti uiui, quae ſine omni dubio ab aeris preſſu
<pb o="73" file="0083" n="83" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
ſuſtinetur, quemadmodum in inſtitutionibus aerome-<lb/>triae §. </s>
  <s xml:id="echoid-s1636" xml:space="preserve">25. </s>
  <s xml:id="echoid-s1637" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s1638" xml:space="preserve">copioſius demonſtraui. </s>
  <s xml:id="echoid-s1639" xml:space="preserve">Aſſumemus ex <lb/>iisdem, quod ſuper ſpatio quadrato pedis rhinlandici, <lb/>qui non multo maior eſt Londinenſi, conſiſtat colu-<lb/>mna aeris, cuius pondus 1958 librarum, et quod graui-<lb/>tas pedis cubici aquae 64 libris aequipolleat. </s>
  <s xml:id="echoid-s1640" xml:space="preserve">(ſupra qui-<lb/>dem c. </s>
  <s xml:id="echoid-s1641" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1642" xml:space="preserve">§. </s>
  <s xml:id="echoid-s1643" xml:space="preserve">37. </s>
  <s xml:id="echoid-s1644" xml:space="preserve">ex Mariottio pondus pedis cubici aquae <lb/>libris 70 Gallicis definiui, quod accipiendum eſt de a-<lb/>quae pede cubico Pariſienſi, quo minor exiſtit pes <lb/>R hinlandicus, hunc autem ideo aſſumere debui, quia <lb/>pondus aeris ipſi accommodatum fuit.) </s>
  <s xml:id="echoid-s1645" xml:space="preserve">Primum quae-<lb/>ratur moles columnae aereae innixae circulo cuius <lb/>diameter 2 {1/2} libr. </s>
  <s xml:id="echoid-s1646" xml:space="preserve">quadratum memoratae diametri eſt <lb/>900 pollicum quadratorum. </s>
  <s xml:id="echoid-s1647" xml:space="preserve">et per §. </s>
  <s xml:id="echoid-s1648" xml:space="preserve">158. </s>
  <s xml:id="echoid-s1649" xml:space="preserve">Inſtit. </s>
  <s xml:id="echoid-s1650" xml:space="preserve">Geo-<lb/>metr. </s>
  <s xml:id="echoid-s1651" xml:space="preserve">1000: </s>
  <s xml:id="echoid-s1652" xml:space="preserve">785 = 906: </s>
  <s xml:id="echoid-s1653" xml:space="preserve">706 poll. </s>
  <s xml:id="echoid-s1654" xml:space="preserve">quadratos circuli, quo <lb/>embolus I. </s>
  <s xml:id="echoid-s1655" xml:space="preserve">terminatur. </s>
  <s xml:id="echoid-s1656" xml:space="preserve">et porro §. </s>
  <s xml:id="echoid-s1657" xml:space="preserve">198. </s>
  <s xml:id="echoid-s1658" xml:space="preserve">Inſtit. </s>
  <s xml:id="echoid-s1659" xml:space="preserve">Geom. <lb/></s>
  <s xml:id="echoid-s1660" xml:space="preserve">144: </s>
  <s xml:id="echoid-s1661" xml:space="preserve">706 = 1958: </s>
  <s xml:id="echoid-s1662" xml:space="preserve">9599 {23/36} libras aeris, quae embolum <lb/>premunt, et facta exhalationum condenſatione redu-<lb/>cunt. </s>
  <s xml:id="echoid-s1663" xml:space="preserve">Tantundem igitur omnes, ex oppoſita parte <lb/>emboli inuerſi attollere poſſunt. </s>
  <s xml:id="echoid-s1664" xml:space="preserve">Trudatur aqua per <lb/>duas fiſtulas diam. </s>
  <s xml:id="echoid-s1665" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1666" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s1667" xml:space="preserve">et altitudinis 100 pedum. </s>
  <s xml:id="echoid-s1668" xml:space="preserve">una <lb/>continet 54 {288/1728} pedes cubicos, duae ſimiles 108 {1/3} ca-<lb/>piunt. </s>
  <s xml:id="echoid-s1669" xml:space="preserve">multiplicato hoc numero per 64 1. </s>
  <s xml:id="echoid-s1670" xml:space="preserve">prodeunt <lb/>6933 librae, quibus a ſumma 9599 lib. </s>
  <s xml:id="echoid-s1671" xml:space="preserve">demtis, ſuperſunt <lb/>2666 lib. </s>
  <s xml:id="echoid-s1672" xml:space="preserve">pro attritu uincendo, qui, uti dixi ob per-<lb/>pendicularem motum @@boli, multo minor eſt, quam <lb/>ſi embolus traheretur obliquius. </s>
  <s xml:id="echoid-s1673" xml:space="preserve">Huic ponderi prae-<lb/>terea accedit uelocitas, quae impetum efficit, et moli <lb/>prementi nouam uim conciliat.</s>
  <s xml:id="echoid-s1674" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1675" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1676" xml:space="preserve">Multitudo aquarum in altum propulſarum ex <lb/>iisdem praemiſſis intelligitur. </s>
  <s xml:id="echoid-s1677" xml:space="preserve">Si enim, in duabus lau-<lb/>datae diametri fiſtulis, motus contingat in perpendi-<lb/>culo 7 pedum, et repetatur decies intra minutum tem-
<pb o="74" file="0084" n="84" rhead="CAPVT IV."/>
poris, uid. </s>
  <s xml:id="echoid-s1678" xml:space="preserve">Lit. </s>
  <s xml:id="echoid-s1679" xml:space="preserve">Q. </s>
  <s xml:id="echoid-s1680" xml:space="preserve">aſſurgent eodem ſpatio cylindri de-<lb/>cem datae altitudinis 7 p. </s>
  <s xml:id="echoid-s1681" xml:space="preserve">in qualibet fiſtula, ſinguli au-<lb/>tem cylindri 7 p. </s>
  <s xml:id="echoid-s1682" xml:space="preserve">capiunt circiter 4 pedes cubicos, ita-<lb/>que intra minutum primum ſurſum pelluntur in rece-<lb/>ptaculum commune 80 pedes cubici. </s>
  <s xml:id="echoid-s1683" xml:space="preserve">Vnus pes cu-<lb/>bicus continet 36 cantharos Pariſienſes, et tales 2880, <lb/>h. </s>
  <s xml:id="echoid-s1684" xml:space="preserve">e. </s>
  <s xml:id="echoid-s1685" xml:space="preserve">dolia decem uno minuto effunduntur. </s>
  <s xml:id="echoid-s1686" xml:space="preserve">hora una <lb/>dolia 600, et horis 24, dolia 14, 400 attolluntur. </s>
  <s xml:id="echoid-s1687" xml:space="preserve">De <lb/>Machina Marlyenſi Cap. </s>
  <s xml:id="echoid-s1688" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1689" xml:space="preserve">§. </s>
  <s xml:id="echoid-s1690" xml:space="preserve">32 dixi, eam diurno ſpa-<lb/>tio 18102 dolia Pariſienſia in ſublime euehere, poſita o-<lb/>mnium partium integritate, atque hinc conſequitur, <lb/>parum abeſſe, quin unica machina Londinenſis tantun-<lb/>dem aquae attollat, quantum uaſtus Marlyacenſis operis <lb/>apparatus. </s>
  <s xml:id="echoid-s1691" xml:space="preserve">Verum quoad altitudinem perpendiculorum <lb/>inſigne diſcrimen eſt, ut ex §. </s>
  <s xml:id="echoid-s1692" xml:space="preserve">26. </s>
  <s xml:id="echoid-s1693" xml:space="preserve">Cap. </s>
  <s xml:id="echoid-s1694" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1695" xml:space="preserve">conſtat. </s>
  <s xml:id="echoid-s1696" xml:space="preserve">Lon-<lb/>dinenſis euehit aquas, in receptaculum plumbeum, <lb/>quod in turris ligneae ſummo eſt, et ſuperficie aqua-<lb/>rum fluminis 124 pedibus altius exiſtit, per duas fiſtulas <lb/>cupreas, quae diametrum 9 uel 10 digitorum habent. <lb/></s>
  <s xml:id="echoid-s1697" xml:space="preserve">Marlyacenſis aquas ultra perpendiculum 500 p. </s>
  <s xml:id="echoid-s1698" xml:space="preserve">pro-<lb/>pellit.</s>
  <s xml:id="echoid-s1699" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1700" xml:space="preserve">10. </s>
  <s xml:id="echoid-s1701" xml:space="preserve">Hanc machinam hydraulicam Londinenſem, <lb/>alteram toto terrarum orbe maximam poſt Marlyen-<lb/>ſem recte cenſeri et uocari, neminem dubitare ſinent <lb/>ea, quae de eius uirtute et aquarum, quas haurit, copia <lb/>inſigni hucusque diſſerui. </s>
  <s xml:id="echoid-s1702" xml:space="preserve">Inprimis ſi illud quoque ob-<lb/>ſeruetur, hodiel duo eiusmodi ahena in iisdem aedibus <lb/>iuxta ſe inuicem, cum cylindris tubisque reſpondenti-<lb/>bus, conſtituta, aquis ex Tameſi extollendis adhiberi. <lb/></s>
  <s xml:id="echoid-s1703" xml:space="preserve">unam tantum quidem machinam ablolutam reperian-<lb/>ni 1726 menſe lulio, ſed altera iam coepta erat, quia <lb/>prior non ſufficiebat, aquis in aedes, quae circa pala-<lb/>tium regium ſitae ſunt, auehendis. </s>
  <s xml:id="echoid-s1704" xml:space="preserve">Interea igitur,
<pb o="75" file="0085" n="85" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
dum altera componebatur, pluribus equis antliae, quae <lb/>aquas attollebant, in motum ciebantur. </s>
  <s xml:id="echoid-s1705" xml:space="preserve">magna etiam <lb/>pars domuum, quae prope pontem ſunt, a machina <lb/>ſub ponte ſuſpenſa aquas recipit. </s>
  <s xml:id="echoid-s1706" xml:space="preserve">in nouam autem ur-<lb/>bis regionem, quae a palatio regio occaſum uerſus por-<lb/>rigitur, aquae deriuantur noua et uix ante biennium fi-<lb/>nita machina, quam quidam Reg. </s>
  <s xml:id="echoid-s1707" xml:space="preserve">Soc. </s>
  <s xml:id="echoid-s1708" xml:space="preserve">Scient. </s>
  <s xml:id="echoid-s1709" xml:space="preserve">ſodalis <lb/>adornaſſe dicitur. </s>
  <s xml:id="echoid-s1710" xml:space="preserve">nimirum uerſus oppidum Chelſeam <lb/>iuxta Tameſin in ſolo argilloſo alueus accliuis quadrin-<lb/>gentos circiter paſſus longus, excauatus eſt, in quem a-<lb/>quae fluminis, quando maris fluxu accumulantur, in-<lb/>grediuntur, et quando fluxus ceſſat, cataracta demiſſa <lb/>earum in flumen reditus prohibetur. </s>
  <s xml:id="echoid-s1711" xml:space="preserve">poſtea refluis a-<lb/>quis ſenſim ſubſidentibus, quaedam cataractae oſtia a-<lb/>periuntur plus minusue, et per eadem aquae in decliui <lb/>alueo proruentes illabuntur in rotas, quarum diameter <lb/>erat circiter 20 pedum, his antliae haurientes premen-<lb/>tesque agitantur, aque ita per fiſtulas antliis annexas <lb/>aquae in aedes non procul inde diſſitas propellun-<lb/>tur.</s>
  <s xml:id="echoid-s1712" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1713" xml:space="preserve">11. </s>
  <s xml:id="echoid-s1714" xml:space="preserve">Inuentum machinae hydraulicae Londinenſis, <lb/>occaſionem dedit Dn. </s>
  <s xml:id="echoid-s1715" xml:space="preserve">Bosfrand, Academiae architectu-<lb/>raeregiae Pariſienſis ſodali, de commodiore et ſimpli-<lb/>ciore compoſitione excogitanda, quam abſoluit ſequen-<lb/>ti modo. </s>
  <s xml:id="echoid-s1716" xml:space="preserve">A eſt fornax, ſupra quam ahenum B ponitur, <lb/>
<anchor type="note" xlink:label="note-0085-01a" xlink:href="note-0085-01"/>
cuius lamina cuprea ſpſſa {1/12} digiti Pariſienſis, idem-<lb/>quae figuram ſphaericam, uel ſuperius inſtar pyri con-<lb/>tractam habet. </s>
  <s xml:id="echoid-s1717" xml:space="preserve">C. </s>
  <s xml:id="echoid-s1718" xml:space="preserve">duo tubi exigui epiſtomiis inſtructi, <lb/>quorum alter in aquas penetrat, alter in ſpatio aere ple-<lb/>no, quod aquae imminet, finitur, pro exceſſu defectu-<lb/>que aquarum inueniendo, uti traditur ſub litera G de-<lb/>ſcriptionis anglicanae. </s>
  <s xml:id="echoid-s1719" xml:space="preserve">E. </s>
  <s xml:id="echoid-s1720" xml:space="preserve">Tubus cupreus, cuius extre-<lb/>mo epiſtomium uerſatile F inſeritur, idemque tubus
<pb o="76" file="0086" n="86" rhead="CAPVT IV."/>
connectitur cum ampliore H, cui infra adhaeret fiſtula <lb/>plumbea aſpirans K, et a latere iungitur alia MN, per <lb/>quam aquae aſcendunt. </s>
  <s xml:id="echoid-s1721" xml:space="preserve">Proportio ſoliditatis uel ca-<lb/>pacitatis aheni B et cylindri H, eſt 6:</s>
  <s xml:id="echoid-s1722" xml:space="preserve">1, quam experien-<lb/>tia confirmauit. </s>
  <s xml:id="echoid-s1723" xml:space="preserve">ut, ſi ahenum 12 pedes cubicos capit, <lb/>cylindrus duos pedes ſolidos ſimiles contineat. </s>
  <s xml:id="echoid-s1724" xml:space="preserve">longi-<lb/>tudo fiſtulae aſpirantis K 24 pedum, et alterius MN <lb/>18 pedum regiorum eſt.</s>
  <s xml:id="echoid-s1725" xml:space="preserve"/>
</p>
<div xml:id="echoid-div22" type="float" level="2" n="2">
<note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">Fig. 19. <lb/>Tab, III.</note>
</div>
<p>
  <s xml:id="echoid-s1726" xml:space="preserve">12. </s>
  <s xml:id="echoid-s1727" xml:space="preserve">Aquarum aſcenſus his legibus fit. </s>
  <s xml:id="echoid-s1728" xml:space="preserve">Cum aquae in <lb/>aheno B calore in uapores reſoluuntur, uapor uehe-<lb/>mentiſſime expanſus, aſſurgit per tubum E, apertoque <lb/>epiſtomio F ingreditur in cylindrum H, ibique aerem <lb/>calore quam maxime attenuatum reddit. </s>
  <s xml:id="echoid-s1729" xml:space="preserve">Clauſo au-<lb/>tem epiſtomio F, admittitur per canalem O, uel quod <lb/>opportunius, per alium P, qui ex uaſe, aquam frigidam <lb/>continente, dependet, aqua frigida, quae dum celeri-<lb/>ter, et quidem per laminam I perforatam, ut in toto <lb/>cylindro aequaliter deffundatur, delabitur, frigore ſuo <lb/>contrahit uaporem, quo in exiguum ſpatium redacto, <lb/>atmoſphaera per fiſtulam plumbeam aſpirantem K, et <lb/>ualuulam extremo R impoſitam, aquas propellit, et <lb/>cylindrum H iisdem fere replet, eoque recepto ualuu-<lb/>la R ſponte relabitur. </s>
  <s xml:id="echoid-s1730" xml:space="preserve">Interim noua incrementa uapor <lb/>cepit, et epiſtomio F conuerſo, tanta ui premit aquas <lb/>intra cylindrum H contentas, ut aperiant ualuulam al-<lb/>teram prope L, et per tubum MN in caſtellum effun-<lb/>dantur.</s>
  <s xml:id="echoid-s1731" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1732" xml:space="preserve">13. </s>
  <s xml:id="echoid-s1733" xml:space="preserve">Hoc opus Dn. </s>
  <s xml:id="echoid-s1734" xml:space="preserve">Auctor reapſe Cachani propẽ <lb/>Lutetiam, exſecutus eſt u. </s>
  <s xml:id="echoid-s1735" xml:space="preserve">quae de eo referuntur in no-<lb/>uis literariis Lipſienſ. </s>
  <s xml:id="echoid-s1736" xml:space="preserve">german. </s>
  <s xml:id="echoid-s1737" xml:space="preserve">a. </s>
  <s xml:id="echoid-s1738" xml:space="preserve">1726. </s>
  <s xml:id="echoid-s1739" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1740" xml:space="preserve">lanuar. </s>
  <s xml:id="echoid-s1741" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1742" xml:space="preserve">10, <lb/>atque ita uim uaporum maximam demonſtrauit. </s>
  <s xml:id="echoid-s1743" xml:space="preserve">In <lb/>principio eam ſic aptauerat, ut idem epiſtomium F <lb/>ſeruiret admittendo uapori et aquae frigidae ex fiſtula
<pb o="77" file="0087" n="87" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
MN petitae, deinceps autem comperit, aquam in MN, <lb/>ex cylindro H a uapore expulſam, ab eodem calorem <lb/>concepiſſe, et ad uaporum condenſationem non ſatis <lb/>idoneam eſſe. </s>
  <s xml:id="echoid-s1744" xml:space="preserve">Quapropter èam ex peculiari recepta-<lb/>culo, qua frigida comprehenditur, deriuandam ſuadet. <lb/></s>
  <s xml:id="echoid-s1745" xml:space="preserve">Et licet fiſtula MN, tantum 18 pedes longa ſit, tamen <lb/>non eſt dubitandum, aquas altius aſſurrecturas, ſi cum <lb/>aheni magnitudine et ignium copia, uaporum expan-<lb/>ſio augeatur. </s>
  <s xml:id="echoid-s1746" xml:space="preserve">Interim ipſe ingenue mihi faſſus eſt, hanc <lb/>machinam anglicana multo inferiorem eſſe, quia ſolo <lb/>uapore, pro aquis protrudendis utitur. </s>
  <s xml:id="echoid-s1747" xml:space="preserve">Interim, quia <lb/>parabilior eſt, utilitate et laude ſua minime deſtituetur.</s>
  <s xml:id="echoid-s1748" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1749" xml:space="preserve">14. </s>
  <s xml:id="echoid-s1750" xml:space="preserve">Idem etiam formam machinae Londinenſis par-<lb/>uam (Modele) ligneam, ſecutus eius delineationem <lb/>Londino allatam, perelegantem compoſuit, cuius con-<lb/>templatione ſaepius in aedibus Dn. </s>
  <s xml:id="echoid-s1751" xml:space="preserve">Bosfrandii fui dele-<lb/>ctatus. </s>
  <s xml:id="echoid-s1752" xml:space="preserve">Et utile omnino uidetur prius exiguam eius-<lb/>modi machinam componere, antequam ad magni et <lb/>pretioſiſſimi operis conſtructionem accedas. </s>
  <s xml:id="echoid-s1753" xml:space="preserve">Ita enim <lb/>fiet, ut fabris nonnullarum partium machinae Londi-<lb/>nenſis conformatio, quae menſuris ſolis uix definiri <lb/>poteſt, diſtinctius ob oculos et ad imitandum proponi <lb/>queat.</s>
  <s xml:id="echoid-s1754" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1755" xml:space="preserve">15. </s>
  <s xml:id="echoid-s1756" xml:space="preserve">Vt autem Lector ipſemet, de diſcrimine machi-<lb/>nae primum a Sauerio inuentae, et eiusdem recentio-<lb/>ris fabricae, iudicare poſſt, inſeram huc quae <emph style="sc">Har-<lb/>risivs</emph> in Lexico technico, ſub titulo Engine, retulit.</s>
  <s xml:id="echoid-s1757" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1758" xml:space="preserve">The other Engine, is for raiſing Water by the force <lb/>
<anchor type="note" xlink:label="note-0087-01a" xlink:href="note-0087-01"/>
of Fire, in which ne (np. </s>
  <s xml:id="echoid-s1759" xml:space="preserve">Savery) hath ſhewed, as great <lb/>Ingenuity, Depth, and Thought, and true mechanick <lb/>Skill, as aver diſcovered it ſelf in any deſign of this na-<lb/>ture. </s>
  <s xml:id="echoid-s1760" xml:space="preserve">the deſcription of this Engine is as follows.</s>
  <s xml:id="echoid-s1761" xml:space="preserve"/>
</p>
<div xml:id="echoid-div23" type="float" level="2" n="3">
<note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">Tab. V. <lb/>Fig. 1.2.3.</note>
</div>
<pb o="78" file="0088" n="88" rhead="CAPVT IV."/>
<p>
  <s xml:id="echoid-s1762" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1763" xml:space="preserve">Denotés two Furnaces, whoſe Fire places are B, 1, <lb/>2, and their Funnel or chimney C. </s>
  <s xml:id="echoid-s1764" xml:space="preserve">in theſe two Furnaces <lb/>are placed two Veſſels of Copper, which he calls Boy-<lb/>lers, the one a larger as L, the other a ſmaller as D. </s>
  <s xml:id="echoid-s1765" xml:space="preserve">Theſe <lb/>Boylers have each a Gage Pipe as G and N, of which G <lb/>goes within eight Inches of the Bottom, but N reaches <lb/>only half way down the great Boyler,</s>
</p>
<p>
  <s xml:id="echoid-s1766" xml:space="preserve">By theſe Pipes, before the Engine can worck, you <lb/>muſt firſt fill the ſmall Boyler quite full, and the great <lb/>Boyler two Thirds full of water. </s>
  <s xml:id="echoid-s1767" xml:space="preserve">Thenlight the Fire <lb/>at B<emph style="sub">1</emph>, and make the water in L boil, by which means <lb/>the Steam of it being, quite confined, muſt needs be <lb/>wonderfully compreſſed, and therefore will, on the <lb/>opening of a way for it to iſſue out, (which is done <lb/>by turning Z the Handle of the regulator from you) <lb/>ruſh with a great Force thro the Steam Pipe O<emph style="sub">1</emph>, into <lb/>the Receiver P<emph style="sub">1</emph>, driving all the Air before it, and for-<lb/>cing it up into the Force Pipe, through the Clack R<emph style="sub">1</emph>, <lb/>as you will perceiue by the Noiſe and Ratling of the <lb/>Clack; </s>
  <s xml:id="echoid-s1768" xml:space="preserve">And when all the Air is thus driven out, the <lb/>Receiver P<emph style="sub">1</emph>, will be very much heated, by the Steam. <lb/></s>
  <s xml:id="echoid-s1769" xml:space="preserve">when you find, that it is throughly emptied, and is <lb/>grown very hot, as you may both ſee and feel, then <lb/>pull the handle of theregulator towards you, by which <lb/>means you will ſtop the ſteam Pipe O<emph style="sub">1</emph>, ſo that no mo-<lb/>re Steam can yet come into it, but you will open it a <lb/>way into O<emph style="sub">2</emph>, and by that means fill the Receiver P<emph style="sub">2</emph>, <lb/>with the Steam, as the other was before. </s>
  <s xml:id="echoid-s1770" xml:space="preserve">While this <lb/>is doing, let ſome cold Water be poured on the Re-<lb/>ceiver P<emph style="sub">1</emph>, by which means the Steam there being coo-<lb/>led, and condenſed, and contracted into a very little <lb/>room, and conſequently preſſing, but very little, (if at <lb/>all) on the Value or Clack R<emph style="sub">1</emph>, at the bottom of the
<pb o="79" file="0089" n="89" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
Receiver P<emph style="sub">1</emph>, There is nothing there to countrebal-<lb/>lance, the preſſure of the Atmoſphere, on the ſurface <lb/>of the Water, in the lower Part of the Suking Pipe T; <lb/></s>
  <s xml:id="echoid-s1771" xml:space="preserve">where fore it will be preſſed up, and aſcend into, and <lb/>fill the Receiver P<emph style="sub">1</emph>, driving out before it as it raiſes, <lb/>the Clack or Valve R<emph style="sub">3</emph>, which afterwards falling down <lb/>again and ſhutting cloſe hinders the deſcent of the wa-<lb/>ter that way. </s>
  <s xml:id="echoid-s1772" xml:space="preserve">Then (the Receiver P<emph style="sub">2</emph>, being in the <lb/>mean time emptied of its Air) turn the handle of the <lb/>Regulator from you, and the Force of the Steam co-<lb/>ming from the Boyler, will be all upon the ſurface of the <lb/>Water contained in the Receiver P<emph style="sub">1</emph>, where it grauita-<lb/>tes or preſſes hard upon it, and ſtill encreaſes, its Spring <lb/>or elaſticity, till it comes to overballance, or exceed <lb/>the Weight of the Water into the Receiver, which <lb/>then it will neceffarly drive up through the Paſſage Q, <lb/>R, Q, Q, into the Force Pipe S, and at laſt diſcharge it <lb/>out at the Top, as you ſee in the Figure.</s>
  <s xml:id="echoid-s1773" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1774" xml:space="preserve">After the very ſame manner, tho alternately, is the <lb/>Receiver P<emph style="sub">2</emph> filled with, and emptied of Water, and <lb/>by this Means a conſtant Steam is kept continually <lb/>running out at the Top of the Force Pipe S, and ſo the <lb/>water is raiſed very eaſily from the bottom of the mine <lb/>etc. </s>
  <s xml:id="echoid-s1775" xml:space="preserve">to the place, where it is deſigned to be diſcharged.</s>
  <s xml:id="echoid-s1776" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1777" xml:space="preserve">Only 1 ſhould add, that after the Engine begins to <lb/>work, and the water is <gap/>ſen into, and hath filled the <lb/>Force Pipe S, then it fills the little Ciſtern X, and by <lb/>that means feeds the Pipe yy, which he calls the con-<lb/>denſing Pipe, becauſe Water is conveyed down from <lb/>thence, to cool the receivers, when troughly heated <lb/>by the Steam, in order to make them Suck (at t'is u-<lb/>ſually called) the Water out of the well up into the <lb/>Receiver.</s>
  <s xml:id="echoid-s1778" xml:space="preserve"/>
</p>
<pb o="80" file="0090" n="90" rhead="CAPVT IV."/>
<p>
  <s xml:id="echoid-s1779" xml:space="preserve">Alſo a little above that ciſtern goes the Pipe E, <lb/>which conveys water from the Force Pipe into D, the <lb/>leſſer Boyler, which is there placed to repleniſh the <lb/>great Boyler L, when the Water in it begins to be al-<lb/>moſt conſumed. </s>
  <s xml:id="echoid-s1780" xml:space="preserve">Now when there is need of doing <lb/>this, turn the Cock E ſo, that there can be no commu-<lb/>nication between the Force Pipe S, and theleſſer Boy-<lb/>ler D, and putting in a little Fire, at B<emph style="sub">2</emph>, the Water the-<lb/>re will grow preſently hot; </s>
  <s xml:id="echoid-s1781" xml:space="preserve">and when it boils, its own <lb/>Steam, which hath no vent out, preſſing on its ſurface, <lb/>will force the Water up the Pipe H, trough K, into <lb/>the great Boyler L, and ſo long will it run, till the ſur-<lb/>face of the Water in the Boyler D, get to be as low, <lb/>as the bottom of the Pipe H, and then the Steam and <lb/>Water will run together, and by its Noiſe and Ratling <lb/>of the Clack 1, will giue him that worcks the Engine, <lb/>ſufficient aſſurance, that D hath emptied and diſchar-<lb/>ged it ſelf into L, and carried in as much Water, as is <lb/>then neceſſary, after which by turning the Cock I a-<lb/>gain, you may let new cold Water out of S into D the <lb/>leſſer Boiler as before: </s>
  <s xml:id="echoid-s1782" xml:space="preserve">and thus will there be a con-<lb/>ſtant motion, and a continual ſupply of the Engine, <lb/>without fear of Decay or diſorder.</s>
  <s xml:id="echoid-s1783" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1784" xml:space="preserve">Alſo to know whether L want repleniſhing or not, <lb/>you need only turn the Cock N, and if Water come <lb/>out, there is no need to repleniſh; </s>
  <s xml:id="echoid-s1785" xml:space="preserve">but if Steam only <lb/>come, you may conclude, there is. </s>
  <s xml:id="echoid-s1786" xml:space="preserve">And the like will <lb/>the Cock G do, in reference to the leſſer Boyler D, <lb/>ſhewing when tis neceſſary to ſypply that with freſh <lb/>water from S, ſo that in working the Engine there is <lb/>very little Skill or labour required, it being only to <lb/>be injured by either a ſtupid, or wilful neglect of the
<pb o="81" file="0091" n="91" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
Uſes and application of this Engine. </s>
  <s xml:id="echoid-s1787" xml:space="preserve">the Reader will <lb/>find a full account in the Inventors Book called the <lb/>Miners Friend.</s>
  <s xml:id="echoid-s1788" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div25" type="section" level="1" n="13">
<head xml:id="echoid-head27" style="it" xml:space="preserve">Interpretatio Latina.</head>
<p>
  <s xml:id="echoid-s1789" xml:space="preserve">Altera machina deſtinata eſt aquis ui ignium extol-<lb/>lendis, circa quam Sauerius inuentor magnam perſpi-<lb/>caciam probauit. </s>
  <s xml:id="echoid-s1790" xml:space="preserve">Deſcriptio eiusdem talis eſt. </s>
  <s xml:id="echoid-s1791" xml:space="preserve">A. <lb/></s>
  <s xml:id="echoid-s1792" xml:space="preserve">Notat duas fornaces, in quibus ignis accenditur in B, <lb/>1. </s>
  <s xml:id="echoid-s1793" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1794" xml:space="preserve">et fumarium C. </s>
  <s xml:id="echoid-s1795" xml:space="preserve">his fornacibus impoſita ſunt duo <lb/>uaſa cuprea, quae lebetes nominat, quorum alter am-<lb/>plior, alter minor et contractior D. </s>
  <s xml:id="echoid-s1796" xml:space="preserve">Quilibet lebes ha-<lb/>bet tubos exploratorios G et N, quorum alter G por-<lb/>rigitur in ahenum, ut 8 digitis a fundo abſit, alter N, <lb/>tantum medium aheni circiter attingit.</s>
  <s xml:id="echoid-s1797" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1798" xml:space="preserve">Antequam machina moueri queat, repletur primum <lb/>aquis lebes paruus totus usque ad ſummum, ſed in ma-<lb/>iore una pars tertia ſpatii contenti uacua relinquitur. <lb/></s>
  <s xml:id="echoid-s1799" xml:space="preserve">tum ſub maiore fiat ignis, ut aquae ebulliant, ita enim <lb/>uapor concluſus magisque continuo efferueſcens, ex-<lb/>pandetur, et per obuiam uiam (aperto epiſtomio Z, <lb/>anſa rectoris propulſa) magna ui per tubum uaporife-<lb/>rum O ingredietur recipientem P, atque aerem omnem <lb/>ante ſe trudet, et per ualuulam R<emph style="sub">1</emph>, in fiſtulam compreſſus <lb/>propellet, quemadmo dum ſtrepitu ualuulae innote-<lb/>ſcet. </s>
  <s xml:id="echoid-s1800" xml:space="preserve">Cumque aer expulſus eſt, recipiens P<emph style="sub">1</emph> uapore <lb/>incaleſcet, et ubi tactu ſenties eum ſatis calidum et aere <lb/>uacuum eſſe, adduces ad te anſam rectoris, et fiſtulam <lb/>uaporiferam O<emph style="sub">1</emph> claudes, ut uapor arceatur, uerum <lb/>una uiam facies uerſus O<emph style="sub">2</emph>, et interim recipientem P<emph style="sub">2</emph> <lb/>replebis uapore. </s>
  <s xml:id="echoid-s1801" xml:space="preserve">Dum hoc fit, demittes aquam fri-<lb/>gidam inrecipientem P<emph style="sub">1</emph>, qua condenſabitur uapor, et
<pb o="82" file="0092" n="92" rhead="CAPVT IV."/>
cum ualuula R<emph style="sub">1</emph> parum prematur, et nihil atmoſphae-<lb/>rae preſſui, in ſuperficies aquae in puteo ſtagnantis, <lb/>obſiſtat, haec per fiſtulam aſpirantem T aſcendet, et <lb/>recipientem P<emph style="sub">1</emph> replebit, ualuula uero R<emph style="sub">3</emph> relabetur et <lb/>deſcenſum aquarum impediet. </s>
  <s xml:id="echoid-s1802" xml:space="preserve">Interea temporis reci-<lb/>piens P2 ab aere uacuabitur, et repulſa anſa rectoris <lb/>uapor magna ui incumbet aquae recipiente P1 conten-<lb/>tae, eiusque ſuperato pondere, eam per QQQ exire, <lb/>et per fiſtulam S aſſurgere et in ſummo exundare co-<lb/>get. </s>
  <s xml:id="echoid-s1803" xml:space="preserve">Et ſimiliter alternate recipiens P2 implebitur et <lb/>uacuabitur aquis, et ita continuo aqua ex fiſtulae S <lb/>ſupremo orificio profluet, et ex imo puteo in locum, <lb/>in quem deſtinata eſt, expelletur. </s>
  <s xml:id="echoid-s1804" xml:space="preserve">Illud addo, ut cum <lb/>machina interiore motu acta, fiſtulam compreſſus ple-<lb/>nam reddidit, paruaj ciſterna X impleaturl, et fiſtula y y, <lb/>quae uocatur condenſationis, nutriatur, ex qua aqua fri-<lb/>gida ad uaporem condenſandum delabitur. </s>
  <s xml:id="echoid-s1805" xml:space="preserve">Paulo ſupra <lb/>ciſternam eſt alia fiſtula E, quae aquam ex fiſtula com-<lb/>preſſus deriuat in paruum lebetem, qui poſitus eſt, ad <lb/>maiorem L replendum, cum aqua maximam partem in <lb/>uaporem eſt reſoluta, quando autem hoc eſt neceſſa-<lb/>rium, ita conuerte epiſtomium E, ut nullum ſuperſit <lb/>commercium, inter fiſtulam compreſſus et paruum le-<lb/>betem D, tum fac exiguum ignem in B2, et aqua ſta-<lb/>tim efferueſcet, et uapor eius exitum non inueniens, <lb/>premet aquae ſuperficiem, ut per K et fiſtulam H in-<lb/>grediatur maiorem lebetem L, tamdiu autem fluet, do-<lb/>nec ſuperficies aquae in lebete D, humilior eſt fundo <lb/>fiſtulae H, tum enim uapor cum aqua mixtus, una pro-<lb/>rumpet, et ſtrepitu indicabit agitari machinam, et a-<lb/>quam ex D in L ſufficienti copia egeſtam eſſe, poſtea <lb/>conuerſo epiſtomio I, denuo aqua frigida ex S in par-
<pb o="83" file="0093" n="93" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
uum lebetem D admittitur, isque motus ſine obſtaculo <lb/>continuabitur.</s>
  <s xml:id="echoid-s1806" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1807" xml:space="preserve">Vt cognitum habeas, utrum lebes L nouam imple-<lb/>tionem deſideret, uerte epiſtomium N, ſi enim aqua <lb/>effluat, indicium erit, eam adhuc ſufficere, ſi uero ua-<lb/>por exeat, aqua infundenda eſt. </s>
  <s xml:id="echoid-s1808" xml:space="preserve">Idemque praeſtat e-<lb/>piſtomium G in lebete minore D, ita ut ad moderan-<lb/>dam hanc machinam exigua peritia aut labor requira-<lb/>tur; </s>
  <s xml:id="echoid-s1809" xml:space="preserve">quemadmodum lector uberius explicatum inue-<lb/>niet in auctoris libro, cui titulus; </s>
  <s xml:id="echoid-s1810" xml:space="preserve">Amicus foſſoris: </s>
  <s xml:id="echoid-s1811" xml:space="preserve">Bre-<lb/>uiter etiam deſcribitur haec machina in Actis Erud. </s>
  <s xml:id="echoid-s1812" xml:space="preserve">Lipſ. <lb/></s>
  <s xml:id="echoid-s1813" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1814" xml:space="preserve">1700. </s>
  <s xml:id="echoid-s1815" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1816" xml:space="preserve">lanuar. </s>
  <s xml:id="echoid-s1817" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1818" xml:space="preserve">29, ſed ita, ut ex illa delineatione <lb/>machinae effectus ſatis intelligi nequeant.</s>
  <s xml:id="echoid-s1819" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1820" xml:space="preserve">16. </s>
  <s xml:id="echoid-s1821" xml:space="preserve">Deſcriptio modo commemorata, quam doctiſſi-<lb/>mus Harriſius ex ipſius auctoris libro repetitam dedit, <lb/>tam luculenta eſt, ut mea illuſtratione indigere haud <lb/>uideatur. </s>
  <s xml:id="echoid-s1822" xml:space="preserve">Illud deſidero, quod tacet, ad quam altitu-<lb/>dinem diſtentus calore uapor aquam compreſſam po-<lb/>tuerit eleuare, quae item ahenorum fiſtularumque pro-<lb/>portio, quantoque igne, uel quanta ignis materia opus <lb/>fuerit, et qua celeritate et copia aquas in altum expu-<lb/>lerit, quoniam ea omnia ad uirium effectuumque com-<lb/>parationem inſtituendam cognitu neceſſaria ſunt. <lb/></s>
  <s xml:id="echoid-s1823" xml:space="preserve">Nonnulla quidem experimentis ſuis prodidit ſupra §. </s>
  <s xml:id="echoid-s1824" xml:space="preserve">9. </s>
  <s xml:id="echoid-s1825" xml:space="preserve"><lb/>ſq. </s>
  <s xml:id="echoid-s1826" xml:space="preserve">laudatus Dn. </s>
  <s xml:id="echoid-s1827" xml:space="preserve">Bosfrand, cuius machina Saverianae ſi-<lb/>milis eſt, uerum utilius eſſet, ſi conſtaret de dimen-<lb/>ſionibus magnae et amplioris illius, quam Saverius fe-<lb/>liciter in fodinis carbonum anglicanis conſtituiſſe di-<lb/>citur. </s>
  <s xml:id="echoid-s1828" xml:space="preserve">Quod uero ad ipſum hoc inuentum in uni-<lb/>uerſum attinet, idem etiamſi ſit ſimplicioris et parabilis <lb/>operis, tamen utilitate et praeſtantia longiſſime cedit
<pb o="84" file="0094" n="94" rhead="CAPVT IV."/>
nouo illi Londinenſi ſuperius late explicato, ſiquidem <lb/>in hoc non ſola uaporis preſſio, ſed columnae atmo-<lb/>ſphaericae, aqueae reſpondentis, pondus celerrimam <lb/>uehementiſſimamque aquarum expulſionem produ-<lb/>cit.</s>
  <s xml:id="echoid-s1829" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1830" xml:space="preserve">17. </s>
  <s xml:id="echoid-s1831" xml:space="preserve">Sauerii machinam ulterius perficere conatus eſt <lb/><emph style="sc">Dionysivs</emph> <emph style="sc">Papinvs</emph> olim mathematum Profeſſor <lb/>Marburgenſis, cuius extat libellus ſub titulo, Ars noua <lb/>ad aquam ignis adminiculo efficaciſſime eleuandam. </s>
  <s xml:id="echoid-s1832" xml:space="preserve">ed. <lb/></s>
  <s xml:id="echoid-s1833" xml:space="preserve">Francoforti ad Moenum A. </s>
  <s xml:id="echoid-s1834" xml:space="preserve">1707. </s>
  <s xml:id="echoid-s1835" xml:space="preserve">in 8. </s>
  <s xml:id="echoid-s1836" xml:space="preserve">plag. </s>
  <s xml:id="echoid-s1837" xml:space="preserve">6. </s>
  <s xml:id="echoid-s1838" xml:space="preserve">et tab. </s>
  <s xml:id="echoid-s1839" xml:space="preserve">aen. </s>
  <s xml:id="echoid-s1840" xml:space="preserve"><lb/>1. </s>
  <s xml:id="echoid-s1841" xml:space="preserve">et praecipua cogitatorum Papinianorum momentare-<lb/>petuntur in Actis Eruditorum Lipſienſibus. </s>
  <s xml:id="echoid-s1842" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1843" xml:space="preserve">1707. </s>
  <s xml:id="echoid-s1844" xml:space="preserve">M. </s>
  <s xml:id="echoid-s1845" xml:space="preserve"><lb/>Septembri. </s>
  <s xml:id="echoid-s1846" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1847" xml:space="preserve">420. </s>
  <s xml:id="echoid-s1848" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s1849" xml:space="preserve">conuenit in eo machina haec cum <lb/>Saveriana, quod immediate uapor trudit piſtillum, cy-<lb/>lindro aeneo accurate aptatum, quo aqua ſubiecta ua-<lb/>lide compreſſa, cogitur in alium ſiphonem, per oſtium, <lb/>cuius ualuula ſurſum mobilis eſt, aſcendere. </s>
  <s xml:id="echoid-s1850" xml:space="preserve">quod ſatis <lb/>eſt, ad eius conditionem ex hucusque explicatis diiu-<lb/>dicandam. </s>
  <s xml:id="echoid-s1851" xml:space="preserve">praefert eam tamen anglicanae Papinus <lb/>cap. </s>
  <s xml:id="echoid-s1852" xml:space="preserve">4, quia ipſius retorta (ahenum Sauerio) in fornace <lb/>prorſus latet, et igne undiquaque ambitur, item quod <lb/>adhibito piſtillo, uapores in antliam irruentes aquae <lb/>frigidae non allidunt, et quod antlia non per ſuctionem <lb/>repletur. </s>
  <s xml:id="echoid-s1853" xml:space="preserve">Enimuero optarem, ut commemoraſſet Pa-<lb/>pinus, quousque hac machina aquae in altitudinem ex-<lb/>tollantur, quanta item ui et celeritate idem praeſtetur, <lb/>quaeque copia aquarum ſurgat. </s>
  <s xml:id="echoid-s1854" xml:space="preserve">Illud mihi conſtat, ex-<lb/>perimentum, quod Caſſellis aliquando inſtituit, ex uoto <lb/>minime ſucceſſiſſe, diſrupto ignium ui aheno, non ſine <lb/>eorum, qui prope adſtabant, maximo periculo. </s>
  <s xml:id="echoid-s1855" xml:space="preserve">Vol-<lb/>uit etiam idem ingenioſus artifex, ut erumpentibus per
<pb o="85" file="0095" n="95" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
foramen aliquod aquis, ab embolo truſis, rotae mola-<lb/>rum agitarentur, de quo diſſerit capite 6 et ſeqq. </s>
  <s xml:id="echoid-s1856" xml:space="preserve">opu-<lb/>ſculi ſui, exiſtimatque unius ope machinae, quatuor <lb/>molas iſtiusmodi, quae flumine ſequanae rotantur, <lb/>moueri poſſe. </s>
  <s xml:id="echoid-s1857" xml:space="preserve">Verum nemo dubitauerit, ſatius eſſe, <lb/>parcere his ambagibus, et ſumtibus, et lapſu aquarum <lb/>fluentium, pro eodem fine facilius obtinendo uti. </s>
  <s xml:id="echoid-s1858" xml:space="preserve">conf. <lb/></s>
  <s xml:id="echoid-s1859" xml:space="preserve">de inuento Papini <emph style="sc">Levpoldi</emph> Theatr. </s>
  <s xml:id="echoid-s1860" xml:space="preserve">machin. </s>
  <s xml:id="echoid-s1861" xml:space="preserve">hy-<lb/>draul. </s>
  <s xml:id="echoid-s1862" xml:space="preserve">Tom. </s>
  <s xml:id="echoid-s1863" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1864" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1865" xml:space="preserve">92. </s>
  <s xml:id="echoid-s1866" xml:space="preserve">93.</s>
  <s xml:id="echoid-s1867" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1868" xml:space="preserve">18. </s>
  <s xml:id="echoid-s1869" xml:space="preserve">Circa idem tempus, quo Saverius inuentum <lb/>ſuum iudicio Societatis Regiae Londini ſubiecit, etiam <lb/><emph style="sc">Amontonivs</emph>, de adhibendo ad machinas mouendas <lb/>igne, conſilia agitavit, et Regiae ſcientiarum Academiae <lb/>Pariſiis aperuit, prouti narratur in Hiſtoria illius Acade-<lb/>miae a. </s>
  <s xml:id="echoid-s1870" xml:space="preserve">1699, p. </s>
  <s xml:id="echoid-s1871" xml:space="preserve">124. </s>
  <s xml:id="echoid-s1872" xml:space="preserve">et ipſe Amontonius machinam ani-<lb/>mo conceptam deſcribit, in commentariis Acad. </s>
  <s xml:id="echoid-s1873" xml:space="preserve">Pa-<lb/>riſ. </s>
  <s xml:id="echoid-s1874" xml:space="preserve">anni eiusdem, p. </s>
  <s xml:id="echoid-s1875" xml:space="preserve">154. </s>
  <s xml:id="echoid-s1876" xml:space="preserve">ſcilicet nixus experimentis, <lb/>quae docent, aerem calore expanſum amplius ſpatium <lb/>affectare, et amplificato elatere poſita ſibi obſtacula co-<lb/>nari repellere, ſequentem machinae alicuius igni agi-<lb/>tandae conſtructionem fieri poſſe arbitratur. </s>
  <s xml:id="echoid-s1877" xml:space="preserve">Fabri-<lb/>cetur ex laminis cupreis rota, inſtar tympani, duplici <lb/>gaudens peripheria, externa, et interna, dimidio radio <lb/>peripheriae maioris terminata. </s>
  <s xml:id="echoid-s1878" xml:space="preserve">intra peripheriam exter-<lb/>nam in duodecim aequales partes, laminis uerſus inter-<lb/>nam peripheriam demiſſis, probeque ferruminatis, <lb/>diuiſam, totidem cellulae aere repletae componantur, <lb/>poſt has intra peripheriam internam dimidio circiter <lb/>interuallo, uerſus centrum totidem aliae cellulae fiant, <lb/>quarum tres aqua repleantur, in lateribus uero cellula-<lb/>rum harum ualuulae ſurſum aperiendae firmentur, et
<pb o="86" file="0096" n="96" rhead="CAPVT IV."/>
denique ex ſingulis cellulis aereis, ad cellulas, quae a-<lb/>quae continendae ſunt deſtinatae, ducantur tubuli, per <lb/>quos aqua eo poſſit aſſurgere. </s>
  <s xml:id="echoid-s1879" xml:space="preserve">Rota ſic abſoluta ex <lb/>axe ſuo ſuſpendatur, ut dum mouetur, cellula aerea in-<lb/>tra aquas infra rotam ſtagnantes tota mergatur, a latere <lb/>autem rotae ignis accendatur, qui cellulam aeris pro-<lb/>ximam ſubito calefacit, ita enim eueniet, ut aer ciſtula <lb/>comprehenſus uehementer expandatur, et rarefactus per <lb/>tubulum antea deſcriptum aſcendat, in cellulam in qua <lb/>aqua ſtagnat, et dum huic incumbit, aqua preſſa ualuu-<lb/>lam, quae hiat in proxime ſuperiorem cellulam, attollet <lb/>et in illam cellulam ingredietur, atque aquam antea in <lb/>cellula haerentem ulterius ſurſum in ſequentes cellulas, <lb/>laxatis earum ualuulis, expellet, hoc facto mutatur ae-<lb/>quilibrium aquae et rotae, aliquo pondere grauatae, et <lb/>rota incipiet gyrari. </s>
  <s xml:id="echoid-s1880" xml:space="preserve">Dum autem incipit gyrum, cel-<lb/>lula aerea deſcendit, et ab ignibus recedens in aquas <lb/>mergitur, ibique refrigeſcit, et aer contentus contrahi-<lb/>tur, atque elaſticae uirtutis impetus ceſſat. </s>
  <s xml:id="echoid-s1881" xml:space="preserve">In locum <lb/>deſcendentis cellulae ſuccedit ſuperior ſequens, etigni-<lb/>bus admouetur, et aer eius expanſus, eundem, de quo <lb/>ante dixi, effectum praeſtat, et eleuatione aquarum in <lb/>cellulis internis continuata, rotationem quoque tympa-<lb/>ni tamdiu, quamdiu ignis prope rotam accenſus eſt, ef-<lb/>ficit. </s>
  <s xml:id="echoid-s1882" xml:space="preserve">De hac fabrica, etſi nondum in uſum tra-<lb/>ducta, tamen auctor eiusdem pollicetur futurum, ut <lb/>auxilio talis rotae, cuius diameter eſt 24 pedum, <lb/>pondus idem eleuetur, quod 39 equi, uel 234 ho-<lb/>mines uix ſuperare poſſent. </s>
  <s xml:id="echoid-s1883" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s1884" xml:space="preserve">p. </s>
  <s xml:id="echoid-s1885" xml:space="preserve">171. </s>
  <s xml:id="echoid-s1886" xml:space="preserve">Verum haec <lb/>conſilia tutius in medio relinquimus, donec experien-<lb/>tiae teſtimonium accedat. </s>
  <s xml:id="echoid-s1887" xml:space="preserve">Illud negari non poteſt, <lb/>Amontonium, dum de huius machinae uiribus inue-
<pb o="87" file="0097" n="97" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
niendis ſolicitus fuit, in uarias incidiſſe obſeruationes, <lb/>quae ad illuſtrandam aerei elateris facultatem ſpectare <lb/>uidentur. </s>
  <s xml:id="echoid-s1888" xml:space="preserve">u. </s>
  <s xml:id="echoid-s1889" xml:space="preserve">g. </s>
  <s xml:id="echoid-s1890" xml:space="preserve">quod calor aquae ebullientis ha-<lb/>beat limites ſuos, quos non ualet ſuperare, et <lb/>quod idem facultatem elateris aerei tantum augeat, <lb/>ut pondus decem digitorum mercurii, amplius, <lb/>quam aer ſolo ſuo pondere naturali incumbens ſuſti-<lb/>net, attollat. </s>
  <s xml:id="echoid-s1891" xml:space="preserve">et poſita ratione grauitatis aquae et mer-<lb/>curii 1: </s>
  <s xml:id="echoid-s1892" xml:space="preserve">14, aequipollet idem calor 11 pedibus 8 digitis <lb/>aquae illius columnae aqueae altae 32 pedes cui geſtan-<lb/>dae pondus atmoſphaerae ſolum ſufficit. </s>
  <s xml:id="echoid-s1893" xml:space="preserve">Ceterum <lb/>manifeſtum quoque eſt ex dictis, Amontonianam <lb/>machinam a Britannica ueteri et noua diuerſam eſſe, <lb/>quia amplificatio elateris aerei, duntaxat eum in finem <lb/>efficitur, ut rota oneribus extollendis aptata circum-<lb/>ducatur.</s>
  <s xml:id="echoid-s1894" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s1895" xml:space="preserve">19. </s>
  <s xml:id="echoid-s1896" xml:space="preserve">Quae hactenus de machina Londinenſi at-<lb/>tuli, Pariſus menſe lanuario anni 1727. </s>
  <s xml:id="echoid-s1897" xml:space="preserve">horis ſubſeciuis <lb/>maxima m partem in ordinem redegi. </s>
  <s xml:id="echoid-s1898" xml:space="preserve">Interim dum <lb/>huius ſcriptionis editio uariis impedimentis tarda-<lb/>tur, edita eſt machinae Londinenſis breuis explica-<lb/>tio in memorabilibus Viennenſibus (Tit. </s>
  <s xml:id="echoid-s1899" xml:space="preserve">das merck-<lb/>würdige Wien, oder Monathliche Vnterredungen <lb/>von Verſchiedenen daſelbſt befindlichen Merckwür-<lb/>digkeiten der Natur und Kunſt) menſe Februario an. </s>
  <s xml:id="echoid-s1900" xml:space="preserve">ei. <lb/></s>
  <s xml:id="echoid-s1901" xml:space="preserve">1727. </s>
  <s xml:id="echoid-s1902" xml:space="preserve">Excerpam hinc nonnulla, quae ad uberiorem il-<lb/>luſtrationem dictorum pertinere uidentur. </s>
  <s xml:id="echoid-s1903" xml:space="preserve">refertur <lb/>pag. </s>
  <s xml:id="echoid-s1904" xml:space="preserve">74. </s>
  <s xml:id="echoid-s1905" xml:space="preserve">hanc machinam Anglicanam primum in ger-<lb/>mania Sereniſſ. </s>
  <s xml:id="echoid-s1906" xml:space="preserve">Landgrauii Haſſiae, Domini <emph style="sc">Caroli</emph>, <lb/>Magni artium Patroni, iuſſu et auſpiciis, Caſſelis ere-<lb/>ctam fuiſſe, a Dn. </s>
  <s xml:id="echoid-s1907" xml:space="preserve">Ioſepho Emanuel Fiſcher, ab Erlachen,
<pb o="88" file="0098" n="98" rhead="CAPVT IV."/>
Conſiliario et Architecto Caelareo an. </s>
  <s xml:id="echoid-s1908" xml:space="preserve">1722. </s>
  <s xml:id="echoid-s1909" xml:space="preserve">poltea <lb/>Iſaacum Potterum Anglum eandem Regiomonti in <lb/>Hungaria, in metallifodina, ob aquarum magnam co-<lb/>piam deſerta, conſtituiſſe, eademque effeciſſe, ut intra <lb/>24 horarum ſpatium, uiginti mille amphorae (Eimer) <lb/>aquarum, ad altitudinem triginta orgyarum, eleuaren-<lb/>tur, et continuata hac actione per biennium, fodinae <lb/>ab aquis ſuperfluis liberarentur, ut denuo ex illis me-<lb/>talla ſucceſſu proſpero effodere liceret. </s>
  <s xml:id="echoid-s1910" xml:space="preserve">Fere eodem <lb/>tempore mandato et ſumtibus Sereniſſ. </s>
  <s xml:id="echoid-s1911" xml:space="preserve">Domini Fran-<lb/>ciſci Adami, S. </s>
  <s xml:id="echoid-s1912" xml:space="preserve">R. </s>
  <s xml:id="echoid-s1913" xml:space="preserve">I. </s>
  <s xml:id="echoid-s1914" xml:space="preserve">Principis a Schwarzenberg, in hor-<lb/>tis Eiusdem Viennae ſimilis, ſed paulo minor machi-<lb/>na hydraulica, igni animata, dirigente opus laudato <lb/>Dn. </s>
  <s xml:id="echoid-s1915" xml:space="preserve">Conſil. </s>
  <s xml:id="echoid-s1916" xml:space="preserve">Fiſchero, abſoluta et ad eleuandas aquas <lb/>fonticulorum adhibita fuit. </s>
  <s xml:id="echoid-s1917" xml:space="preserve">cuius tantum hic menſu-<lb/>ras et effectus repetam. </s>
  <s xml:id="echoid-s1918" xml:space="preserve">Lebes eſt cupreus rotundus, <lb/>ſpiſſitudinem talem habens, qualis iis tribuitur, qui co-<lb/>quendae cereuiſiae inſeruiunt. </s>
  <s xml:id="echoid-s1919" xml:space="preserve">ſub eo ita Dn. </s>
  <s xml:id="echoid-s1920" xml:space="preserve">Fiſcher <lb/>ignem ſupponere docuit, ut circa lebetem bis moueatur, <lb/>antequam per fumarium egrediatur, ita enim reliquum <lb/>in fumo calorem ueluti elici ex eodem poſſe creditur. <lb/></s>
  <s xml:id="echoid-s1921" xml:space="preserve">Opus habet, pro igne per 24 horas nutriendo, una et <lb/>dimidia ligni mollioris orgyia. </s>
  <s xml:id="echoid-s1922" xml:space="preserve">diameter eius eſt 6 pe-<lb/>dum. </s>
  <s xml:id="echoid-s1923" xml:space="preserve">aqua impletur circiter ad tres partes quartas ſuae <lb/>capacitatis. </s>
  <s xml:id="echoid-s1924" xml:space="preserve">Cylindrus aheno imminens, exaere fuſus <lb/>eſt, altus 9 pedes, diametrum habens 2 pedum, pondus <lb/>eius eſt 1200 librarum. </s>
  <s xml:id="echoid-s1925" xml:space="preserve">embolus metallicus in hoc cy-<lb/>lindro mobilis intra temporis minutum quindecies, in <lb/>perpendiculo ſex pedum ſurſum deorſumque mouetur. </s>
  <s xml:id="echoid-s1926" xml:space="preserve"><lb/>Vectis ſiue librile antlias agitans longum eſt 24 pedes, <lb/>latum 2 p. </s>
  <s xml:id="echoid-s1927" xml:space="preserve">ſpiſſum 18 digitos. </s>
  <s xml:id="echoid-s1928" xml:space="preserve">ex centro eius deſcripti <lb/>ſunt arcus, alti 8 pedes, quibus catenae embolos tra-
<pb o="89" file="0099" n="99" rhead="DE MACHINA HYDRAVL. LONDINENSI."/>
hentes incumbunt. </s>
  <s xml:id="echoid-s1929" xml:space="preserve">Catenae articuli longi ſunt 6 di-<lb/>gitos, ſpiſſi 1 {1/2} digitum. </s>
  <s xml:id="echoid-s1930" xml:space="preserve">antliae haurientis embolus ha-<lb/>bet diametrum 6 {1/2} dig. </s>
  <s xml:id="echoid-s1931" xml:space="preserve">ferrum quod ducit embolum <lb/>cylindri aenei, priſmaticum eſt, et ſpiſſitudine gaudet <lb/>duorum digitorum. </s>
  <s xml:id="echoid-s1932" xml:space="preserve">Quod effectum attinet, machina <lb/>poſterior mediocris magnitudinis eleuat intra 24 horas <lb/>amphoras aquae 11880, ad altitudinem perpendicularem <lb/>75 pedum, et unus homo ſufficit ignibus cuſtodiendis <lb/>et dirigendae machinae. </s>
  <s xml:id="echoid-s1933" xml:space="preserve">et ſi cylindro aeneo diameter <lb/>32 digitorum tribueretur, futurum putatur, ut tantum <lb/>aquae machina attollat, quantum non moueret robur <lb/>centum equorum. </s>
  <s xml:id="echoid-s1934" xml:space="preserve">Dn. </s>
  <s xml:id="echoid-s1935" xml:space="preserve">Fiſcher ita uoluit inſtrui machi-<lb/>nam, ut pluribus antliis ſimul mouendis ſufficeret. <lb/></s>
  <s xml:id="echoid-s1936" xml:space="preserve">quamobrem in literis ad Leupoldum Viennae. </s>
  <s xml:id="echoid-s1937" xml:space="preserve">23 lanuar. </s>
  <s xml:id="echoid-s1938" xml:space="preserve"><lb/>a. </s>
  <s xml:id="echoid-s1939" xml:space="preserve">1725 datis ſic ſcribit: </s>
  <s xml:id="echoid-s1940" xml:space="preserve">Was unſere Feuer - Machine <lb/>anbelanget, ſo brennet ſolche drey Clafftern Holtz <lb/>des Tages, und hat eine Krafft 25 Satz - Röhren, iede <lb/>von 6 Zoll im diameter, und vier Claffter lang zu he-<lb/>ben, oder zu regieren, mit einer Geſchwindigkeit, <lb/>das wenigſtens 14 Hub, ieder von 6 Schuh; </s>
  <s xml:id="echoid-s1941" xml:space="preserve">hoch, in <lb/>einer Minute geſchehe. </s>
  <s xml:id="echoid-s1942" xml:space="preserve">Zum Exempel, wenn das <lb/>Waſſer nicht höher als 4 Clafftern hoch zu heben, ſo <lb/>kan die Machine alle 25 Satz Röhren oder Kolben ſo <lb/>neben einander ſtehen, auf einmahl heben, und alſo 25 <lb/>Ausguſſ - Waſſer in dem Hub produciren. </s>
  <s xml:id="echoid-s1943" xml:space="preserve">Iſt aber <lb/>das Waſſer auf 100 Claſſtern zu heben, ſo müſſen die <lb/>25 Satz - Röhren unter einander, an ſtatt neben einan-<lb/>der geſetzt werden, alſo das nur einen Ausguſſ jeder <lb/>Hub giebet, als den oberſten, weil die unterſten nicht <lb/>zu zehlen ſind.</s>
  <s xml:id="echoid-s1944" xml:space="preserve"/>
</p>
<pb o="90" file="0100" n="100" rhead="CAP. IV. DE MACH. HYDR. LONDINENSI."/>
<p>
  <s xml:id="echoid-s1945" xml:space="preserve">20. </s>
  <s xml:id="echoid-s1946" xml:space="preserve">Ita finio tractationem, de praecipuis machi-<lb/>nis hydraulicis, quas in itinere curioſius contemplari <lb/>et dimetiri licuit. </s>
  <s xml:id="echoid-s1947" xml:space="preserve">Potuiſſem augere earum numerum <lb/>nonnullis aliis argumenti ſimilis, uel addere deſcri-<lb/>ptionem inuentorum mechanicorum, quae partim <lb/>publicis, partim priuatis in technophylaciis, (quae in-<lb/>ter praecipuo loco referri meretur Truchetianum, <lb/>quod Pariſiis eſt in coenobio Carmelitarum) obuia <lb/>habui. </s>
  <s xml:id="echoid-s1948" xml:space="preserve">Enimuero cum laudata in ſuperioribus capi-<lb/>tibus machinamenta, ceteris omnibus quae excogita-<lb/>ta ſunt, longiſſime antecellant, ut tutiſſima promtiſſi-<lb/>maque, ad ciendas in motum aquas, adiumenta, com-<lb/>plecti, atque adeo ad totam pragmatiam hydrau-<lb/>licam inſtruendam, et ubique proſpero ſucceſſu ex-<lb/>ercendam, ualere uideantur, malui a minoris mo-<lb/>menti operibus late recenſendis in praeſenti abſti-<lb/>nere. </s>
  <s xml:id="echoid-s1949" xml:space="preserve">Inprimis cum cauendum mihi eſſet, ne mul-<lb/>titudine picturarum ſumtuoſior et difficilior tractatus <lb/>huius editio redderetur.</s>
  <s xml:id="echoid-s1950" xml:space="preserve"/>
</p>
<pb o="91" file="0101" n="101"/>
</div>
<div xml:id="echoid-div26" type="section" level="1" n="14">
<head xml:id="echoid-head28" xml:space="preserve">SVMMA <lb/>ARGVMENTORVM <lb/>TRACTATVS HYDRAVLICI <lb/><emph style="sc">Praefatio</emph> <lb/>DE <lb/>VTILITATE EX CONTEMPLATIONE <lb/>MACHINARVM IAM CONSTRVCTARVM <lb/>CAPIENDA NEC NON DE INSTITVTI <lb/>RATIONE. <lb/>CAPVT I. <lb/>DE <lb/>MACHINA MARLYENSI</head>
<note style="it" position="right" xml:space="preserve"> <lb/>1. De Inuentore eiusdem. <lb/>2. Tentamen conſtructionis primae deſcribi-<lb/>tur. <lb/>3. De rotis, quae flumini opponuntur, et alueo <lb/>nauigationi deſtinato. <lb/>4. Explicatur ichnographia totius machinae. <lb/>5. De riuis, in quibus rotae ſuſpenſae ſunt. <lb/>6. Situs et magnitudo rotarum. <lb/>7. De diuerſitate antliarum, quae in Machina <lb/>Marlyenſi adhibentur, et ſpeciatim de aſpi-<lb/>rante. <lb/>8. De antlia aſpirante et premente. <lb/>9. De antlia inuerſa.
<pb o="92" file="0102" n="102"/>
10. De emendando uitio embolorum inuerſorum. <lb/>11. De fiſtulis machinae aptatis. <lb/>12. De fiſtularum coniunctione et curuatione. <lb/>13. 14. De officio rotarum, ſpeciatim quoad catenas. <lb/>15. De motu antliarum. <lb/>16. De antlia aſpirante, quae prementibus iun-<lb/>gitur. <lb/>17. Deſcriptio antliarum et motus earundem. <lb/>18. De patellis aeneis, in quibus axes rotantur. <lb/>19. 20. De catenis uerſus aquaeductum tendenti-<lb/>bus, earumque copulatione et motu. <lb/>21. Quomodo moueant catenae antlias eaſtello-<lb/>rum ſuperiorum. <lb/>22. De ſtagno, in quo aquae colliguntur. <lb/>23. De antliis, quibus in caſtellis mediis aquae <lb/>eleuantur. <lb/>24. De fiſtulis, quae aquas ex caſtellis mediis <lb/>in ſupremum deducunt. <lb/>25. De antliis caſtelli ſupremi. <lb/>26. De fiſtulis, aquas in aquaeductum ingeren-<lb/>tibus. <lb/>27. De ipſo aquaeductu. <lb/>28. Quorſum canales aquaeductu deriuentur. <lb/>29. De quantitate materiae, quae in exſtructio-<lb/>ne machinae marlyenſis conſumta fuit, nec <lb/>non de tempore, intra quod abſoluta eſt. <lb/>30. Quod difficultate non careat negotium, ſi
<pb o="93" file="0103" n="103"/>
quis ſingularum illius operis partium fines <lb/>cognoſcere laboret. Subiungitur deſcriptio <lb/>generalis totius machinae. <lb/>31. De quantitate aquarum tot antliis hauſta-<lb/>rum generatim. <lb/>32. De quantitate eadem ſpeciatim rationibus <lb/>rite ſubductis inuenienda. <lb/>33. De uiribus, quae in machinis hydraulcis ſpe-<lb/>ctantur, et difficultatibus, quae in earum <lb/>conſideratione occurrunt. <lb/>34. De oneribus in machina Marlyenſi mouen-<lb/>dis, quantum attinet ad antlias prope <lb/>rotas. <lb/>35. De oneribus, quae uincuntur a catenis et ant-<lb/>liis, quas agitant. <lb/>36. De hypotheſibus ſiue datis, ad fluminis impe-<lb/>tum aeſtimandum neceſſariis. <lb/>37. Calculus uirium pro rotis ſingulis et machi-<lb/>na uniuerſa. <lb/>38. De diuerſa aquarum eiusdem fluminis uelo-<lb/>citate <lb/>39. De aeſtimando attritu. <lb/>40. Cur nonnulla machinae membra ſint laxius <lb/>inter ſe copulata. <lb/></note>
</div>
<div xml:id="echoid-div27" type="section" level="1" n="15">
<pb o="(94)" file="0104" n="104"/><head xml:id="echoid-head29" xml:space="preserve">CAPVT II.
DE <lb/>MACHINIS HYDRAVLICIS <lb/>QVIBVS <lb/>PARISIIS <lb/>AQVAE EX SEQVANA FLVVIO <lb/>HAVRIVNTVR.</head>
<note style="it" position="right" xml:space="preserve"> <lb/>1. De rotis machinae ſub ponte B. Virginis et <lb/># eorum dimenſione. <lb/>2. 3. Dimenſio rotarum dentatarum connexarum. <lb/>4. 5. Antliarum compoſitio ſingularis. <lb/>6. Quomodo rotae demittantur et eleuentur? <lb/>7. Quomodo motus earum cobibeatur? <lb/>8. 9. Quantum aquae his antliis extollatur? <lb/>10. De deſcenſu aquarum bauſtarum per fiſtulas. <lb/>11. 12. De uiribus, quibus laudata machina moue-<lb/># tur. <lb/>13. De Machina bydraulica iuxta pontem no-<lb/># uum Pariſiis firmata et conſtructionerotae <lb/># eiusdem. <lb/>14. De quantitate aquarum bac rota eleuata-<lb/># rum. <lb/>15. De uirium comparatione cumbiſce oneribus. <lb/>16. Quorſum bae aquae deriuentur, et de aquae-<lb/># ductu Arcelienſi. <lb/></note>
</div>
<div xml:id="echoid-div28" type="section" level="1" n="16">
<pb o="(95)" file="0105" n="105"/><head xml:id="echoid-head30" xml:space="preserve">CAPVT III.
DE DVABVS MOLETRINIS <lb/>HYDRAVLICIS <lb/>QVARVM ALAE VENTO VERSANTVR.</head>
<note style="it" position="right" xml:space="preserve"> <lb/>1. De machinis bydraulicis uento agitatis gene-<lb/># ratim et de Batauorum molis pratenſibus. <lb/>2. De loco ubi moletrinae duae bydraul. colloca-<lb/># tae ſunt, et aquarum eodem affluxu. <lb/>3. De alis moletrinae primae. <lb/>4. De freno earundem. <lb/>5. De embolis antliarum prementium. <lb/>6. De regimine motus eorundem. <lb/>7. De perpendiculo motus eorundem. <lb/>8. De fiſtulis, per aquas aquae hauſtae ducuntur. <lb/>9. De copia aquarum bauſtarum. <lb/>10. De fiſtula, per quam aer exturbatur. <lb/>11. Alterius moletrinae alatae deſcriptio. <lb/>12. De praeſtantia eius prae priore. <lb/>13. Quanti haec opera fecerit Petrus l. Ruſſorum <lb/># Imperator?</note>
</div>
<div xml:id="echoid-div29" type="section" level="1" n="17">
<head xml:id="echoid-head31" xml:space="preserve">CAPVT IV. <lb/>DE MACHINA HYDRAVLICA <lb/>LONDINENSI <lb/>IN QVA VIS IGNIS AQVAS IN VAPORES <lb/>RESOLVENTIS CONSPICVA EST.</head>
<note style="it" position="right" xml:space="preserve"> <lb/>1. Agitur de eius inuentore, et ſubiicitur deſeri-<lb/># ptio, quae anglico ſermone prodiit, in lati-<lb/># num conuerſa.
<pb o="96" file="0106" n="106"/>
2. Quomodo ad ſimplicitatem eius compolitio <lb/># reuocari queat, docetur. <lb/>3. Emendatio Deſaguilierii deſcribitur. <lb/>4. De menſuris eius. <lb/>5. De antliis inuerſis adeam applicatis. <lb/>6. Quod antliae inuerſae aſpirantibus praeſtent. <lb/>7. De uiribus buius machinae, et ſigillatim de ui <lb/># uaporum expanſorum. <lb/>8. De pondere aeris hic conſpicuo et eius effectu. <lb/>9. De multitudine aquarum in altum propulſarum. <lb/>10. Quod recte haec machina bydraulica altera <lb/># toto terrarum orbe maxima nominetur, nec <lb/># non de noua quadam machina bydraulica <lb/># prope Londinum conſtructa. <lb/>11. De imitatione Machinae Britannicae Pari-<lb/># ſiis tentata. <lb/>12. 13. 14. Plenior illius explicatio. <lb/>15. Deſcriptio ueteris machinae Sauerianae An-<lb/># glica et latina. <lb/>16. Comparatur Sauerii inuentum cum machina <lb/># recentiore. <lb/>17. De conatibus Papini, pro ſimili machina <lb/># componenda. <lb/>18. Inuentum Amontonii, pro circumagenda ae-<lb/># re rarefacto rota, deſcrilitur. <lb/>19. De machina Britannica Regiomonti Hunga-<lb/># riae, et Viennae Auſtriae erecta diſſeritur. <lb/>20. Epilogus.</note>
<pb file="0107" n="107"/>
  <figure>
    <image file="0107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0107-01"/>
  </figure>
<pb file="0107a" n="108"/>
  <figure>
    <image file="0107a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0107a-01"/>
  </figure>
<pb file="0108" n="109"/>
<pb file="0109" n="110"/>
  <figure>
    <image file="0109-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0109-01"/>
  </figure>
<pb file="0109a" n="111"/>
  <figure>
    <image file="0109a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0109a-01"/>
  </figure>
<pb file="0110" n="112"/>
<pb file="0111" n="113"/>
  <figure>
    <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0111-01"/>
  </figure>
<pb file="0111a" n="114"/>
  <figure>
    <image file="0111a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0111a-01"/>
  </figure>
<pb file="0112" n="115"/>
<pb file="0113" n="116"/>
  <figure>
    <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/>
  </figure>
<pb file="0113a" n="117"/>
  <figure>
    <image file="0113a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113a-01"/>
  </figure>
<pb file="0114" n="118"/>
<pb file="0115" n="119"/>
  <figure>
    <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01"/>
  </figure>
<pb file="0115a" n="120"/>
  <figure>
    <image file="0115a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115a-01"/>
  </figure>
<pb file="0116" n="121"/>
</div>
<div xml:id="echoid-div30" type="section" level="1" n="18">
<pb o="726" file="0117" n="122"/><head xml:id="echoid-head32" xml:space="preserve">10. FRIDER. WEIDLERI
INSTITVTIONES</head>
<head xml:id="echoid-head33" xml:space="preserve">GEOMETRIAE <lb/>SVBTERRANEAE.</head>
  <figure>
    <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0117-01"/>
  </figure>
</div>
<div xml:id="echoid-div31" type="section" level="1" n="19">
<head xml:id="echoid-head34" xml:space="preserve">CVM FIGVRIS AENEIS.</head>
<head xml:id="echoid-head35" xml:space="preserve">VITEMBERGAE <lb/>APVD VIDVAM GERDESIAM.</head>
<head xml:id="echoid-head36" xml:space="preserve">A. C. M D CC XX VI.</head>
<pb file="0118" n="123"/>
</div>
<div xml:id="echoid-div32" type="section" level="1" n="20">
<pb file="0119" n="124"/><head xml:id="echoid-head37" xml:space="preserve">PRAEFATIO.</head>
<p style="it">
  <s xml:id="echoid-s1951" xml:space="preserve">Ad artes inueniendas et ampliſi-<lb/>candas, nulla re magis, quam <lb/>ſpe utilitatis, animi mortalium <lb/>inflammantur. </s>
  <s xml:id="echoid-s1952" xml:space="preserve">Teſtis aegyptus, <lb/>in qua nili inundationes geome-<lb/>triam pepererunt. </s>
  <s xml:id="echoid-s1953" xml:space="preserve">Et in germa-<lb/>nia, poſtquam abditae olim omnis generis metallorum <lb/>uenae, abbinc pluribus ſeculis detectae et perueſtiga-<lb/>tae ſunt, occaſio ſuppeditata eſt, geometriam ad <lb/>ſpecus ſubterraneos metiendos accommodandi. </s>
  <s xml:id="echoid-s1954" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>
Haec ars etiamſi inter noſtros foſſores egregie flore-<lb/>at, tamen cum, ob faſtidia et pericula, quibus ſtipa-<lb/>ta eſt, plerumqne tantum tractetur a pragmaticis, <lb/>mathematicarum ſcientiarum minus gnaris, et pro-<lb/>pterea ab ipſis obſcurius nec ſolide ſatis tradatur, <lb/>feci periculum, eiusdem paulo accuratius formandae <lb/>et ex purae matheſeos principiis demonſtrandae.</s>
  <s xml:id="echoid-s1955" xml:space="preserve">
<pb o="4" file="0120" n="125" rhead="PRAEFATIO."/>
Hic ſcopus eſt praeſentis opuſculi, quod ſpero eo minus <lb/>improbatum iri eruditis, quo rariores de illo argu-<lb/>mento ſcriptores eſſe conſtat. </s>
  <s xml:id="echoid-s1956" xml:space="preserve"># Conſtitueram idem <lb/>inſerere inſtitutionibus mathematicis, poſt bydrau-<lb/>licam, uerum, ob rationes §. </s>
  <s xml:id="echoid-s1957" xml:space="preserve">42. </s>
  <s xml:id="echoid-s1958" xml:space="preserve">ibidem, p. </s>
  <s xml:id="echoid-s1959" xml:space="preserve">646. <lb/></s>
  <s xml:id="echoid-s1960" xml:space="preserve">commemoratas, malui ſeparatim edere, et numeros, <lb/>quibus triangula commode ſoluuntur, ſubiungere. </s>
  <s xml:id="echoid-s1961" xml:space="preserve"><lb/>Ceterum illud quoque lectorem latere nolo, me, huius <lb/>tractationis rectius ſuſcipiendae cauſa, ſuperiore aeſta-<lb/>te Freibergam, montanarum miſniae urbium prin-<lb/>cipem, petiiſſe, et non ſolum in profundas, quae a S. </s>
  <s xml:id="echoid-s1962" xml:space="preserve"><lb/>Laurentio nomen habent, fodinas deſcendiſſe, eas-<lb/>demque et reliquum metallicae rei apparatum lu-<lb/>ſtraſſe, ſed etiam ſpeciatim de cryptarum dimenſione <lb/>illuſtranda, cum peritiſſimis illius artificii uiris <lb/>egiſſe, et eorum obſeruatis inſtitutiſque profeciſſe. </s>
  <s xml:id="echoid-s1963" xml:space="preserve"><lb/>Dab. </s>
  <s xml:id="echoid-s1964" xml:space="preserve">Vitembergae. </s>
  <s xml:id="echoid-s1965" xml:space="preserve">Non. </s>
  <s xml:id="echoid-s1966" xml:space="preserve">lanuar. </s>
  <s xml:id="echoid-s1967" xml:space="preserve">A. </s>
  <s xml:id="echoid-s1968" xml:space="preserve">1726.</s>
  <s xml:id="echoid-s1969" xml:space="preserve"/>
</p>
<note position="foot" xml:space="preserve">PETRVS RAMVS Scholar. mathem. Lib. 2. p. m. 63. Sequentem <lb/>in modum de arte laudata loquitur: Cum itaque de mundi nobilibus <lb/>ſcholis, ſtudioſe mortales omnes, qui aliunde peregre ad nos rediiſſent, <lb/>percunctarer, nulla in gente tam multas mathematici ſludii ſcholas <lb/>comperiebam, publicis ſtipendiis c@natas, quam in germania, cauſamque <lb/>unam eſſe ſubterranea illa audiebam plutonis regna, quod maxima, <lb/>principibus et liberis ciuitatibus penderentur tributa, e fodinis auri <lb/>argentique et ceterorum metallorum, quae geometrico innumerabilium <lb/>machinarum artificio praecipue ſuſtinerentur, ac ſarcirentur.</note>
<pb o="5" file="0121" n="126" rhead="GEOMETRIA SUBTERRANEA."/>
</div>
<div xml:id="echoid-div33" type="section" level="1" n="21">
<head xml:id="echoid-head38" xml:space="preserve">DEFINITIO I.</head>
<p>
  <s xml:id="echoid-s1970" xml:space="preserve">1. </s>
  <s xml:id="echoid-s1971" xml:space="preserve">Geometria ſubterranea eſt ars fodinas metiendi. <lb/></s>
  <s xml:id="echoid-s1972" xml:space="preserve">Germanis uocatur die Marckſcheide - Kunſt.</s>
  <s xml:id="echoid-s1973" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div34" type="section" level="1" n="22">
<head xml:id="echoid-head39" xml:space="preserve">DEFINITIO II.</head>
<p>
  <s xml:id="echoid-s1974" xml:space="preserve">2. </s>
  <s xml:id="echoid-s1975" xml:space="preserve">Totum hoc artificium commode ad tria praecipua <lb/>poteſt reuocari capita. </s>
  <s xml:id="echoid-s1976" xml:space="preserve">Primum agit de dimenſione <lb/>cryptarum, tum qua inclinationem ad horizontem, tum <lb/>qua directionem ad mundi plagas. </s>
  <s xml:id="echoid-s1977" xml:space="preserve">Alterum docet mo-<lb/>dum accedendi ad easdem, tum ex terrae ſuperficie, tum ex <lb/>locis ſubterraneis, adeoque de diſtantiis puncti fodinae <lb/>cuiuslibet, a dato ſupra, uel infra terram, puncto diſquirit. <lb/></s>
  <s xml:id="echoid-s1978" xml:space="preserve">Tertium ſpectat ad deſcriptiones fodinarum ichnographicas, <lb/>orthographicas et ſcenographicas.</s>
  <s xml:id="echoid-s1979" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div35" type="section" level="1" n="23">
<head xml:id="echoid-head40" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s1980" xml:space="preserve">3. </s>
  <s xml:id="echoid-s1981" xml:space="preserve">Inde fluit, tum uſus huius artis ingens, tum officium men-<lb/>ſoris. </s>
  <s xml:id="echoid-s1982" xml:space="preserve">Nempe debet ille 1) Definire ſpatia, intra quae me-<lb/>talla quaerere alicui eſt conceſſum. </s>
  <s xml:id="echoid-s1983" xml:space="preserve">2) Monſtrare acceſſum <lb/>proximum ad ſpecus. </s>
  <s xml:id="echoid-s1984" xml:space="preserve">Indicare uias, per quas aquae e fodinis <lb/>adduci queant. </s>
  <s xml:id="echoid-s1985" xml:space="preserve">4) Determinare extenſiones, capita et concurſus <lb/>uenarum et fibrarum metallicarum. </s>
  <s xml:id="echoid-s1986" xml:space="preserve">5) Promouere circulum aeris <lb/>in fodinis, et exhalationem uaporum noxiorum, et quae ſunt ſimi-<lb/>lia. </s>
  <s xml:id="echoid-s1987" xml:space="preserve">Vide plura de officio menſoris in G<emph style="sc">EORG.</emph> <emph style="sc">Engel</emph>-<lb/><emph style="sc">HARDTI</emph> <emph style="sc">Loehneys</emph>, Bericht vom Bergwerck. </s>
  <s xml:id="echoid-s1988" xml:space="preserve">f. </s>
  <s xml:id="echoid-s1989" xml:space="preserve">212. </s>
  <s xml:id="echoid-s1990" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s1991" xml:space="preserve">et <lb/>A<emph style="sc">BR. A</emph> <emph style="sc">Schoenberg</emph>, Berginformation. </s>
  <s xml:id="echoid-s1992" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s1993" xml:space="preserve">Lipſ. </s>
  <s xml:id="echoid-s1994" xml:space="preserve">1693. <lb/></s>
  <s xml:id="echoid-s1995" xml:space="preserve">f. </s>
  <s xml:id="echoid-s1996" xml:space="preserve">fol. </s>
  <s xml:id="echoid-s1997" xml:space="preserve">110.</s>
  <s xml:id="echoid-s1998" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div36" type="section" level="1" n="24">
<head xml:id="echoid-head41" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s1999" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2000" xml:space="preserve">De hac arte pauca hucusque ſcripta prodierunt. </s>
  <s xml:id="echoid-s2001" xml:space="preserve"><emph style="sc">Georgivs</emph> <lb/><emph style="sc">Agricola</emph>, in praectaro opere de re metallica Baſileae a. <lb/></s>
  <s xml:id="echoid-s2002" xml:space="preserve">1556. </s>
  <s xml:id="echoid-s2003" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2004" xml:space="preserve">libro V. </s>
  <s xml:id="echoid-s2005" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2006" xml:space="preserve">88. </s>
  <s xml:id="echoid-s2007" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2008" xml:space="preserve">nonnulla de dimenſione fodinarum affert, <lb/>ſed tantum generalia, ex quibus intelligitur, eam artem magis ex
<pb o="6" file="0122" n="127" rhead="GEOMETRIA SUBTERRANEA."/>
eo tempore excultam atque elaboratam fuiſſe. </s>
  <s xml:id="echoid-s2009" xml:space="preserve">D. </s>
  <s xml:id="echoid-s2010" xml:space="preserve"><emph style="sc">Erasmvs</emph> <lb/><emph style="sc">Reinholdvs</emph>, Medicus Salueldenſis, Eraſmi aſtronomi filius, <lb/>Erfurti a. </s>
  <s xml:id="echoid-s2011" xml:space="preserve">1574. </s>
  <s xml:id="echoid-s2012" xml:space="preserve">in 4. </s>
  <s xml:id="echoid-s2013" xml:space="preserve">librum germanicum edidit, ſub titulo, <lb/>Vom Marckſcheiden kurtzer und gründlicher Unterricht. </s>
  <s xml:id="echoid-s2014" xml:space="preserve">Qui <lb/>geometriae eiusdem germanicae ſubiungitur, et poſtea a. </s>
  <s xml:id="echoid-s2015" xml:space="preserve">1615. <lb/></s>
  <s xml:id="echoid-s2016" xml:space="preserve">Francf. </s>
  <s xml:id="echoid-s2017" xml:space="preserve">ad M. </s>
  <s xml:id="echoid-s2018" xml:space="preserve">recuſus eſt. </s>
  <s xml:id="echoid-s2019" xml:space="preserve">capit 14. </s>
  <s xml:id="echoid-s2020" xml:space="preserve">plagulas. </s>
  <s xml:id="echoid-s2021" xml:space="preserve">In eodem quidem <lb/>latius, quam <emph style="sc">Agricola</emph>, agit de propoſita materia, ſed 1. </s>
  <s xml:id="echoid-s2022" xml:space="preserve">ta-<lb/>bulas, quae ad inueniendam baſin et perpendicularem trigoni <lb/>rectanguli, laborioſo calculo applicantur, habet. </s>
  <s xml:id="echoid-s2023" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2024" xml:space="preserve">loco libellae, <lb/>quadrante multo incommodiore utitur. </s>
  <s xml:id="echoid-s2025" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2026" xml:space="preserve">Compaſſum pen-<lb/>ſilem penitus ignorat, atque ita per ambages quaerit, quod <lb/>hodie certius per compendium cognoſcitur. </s>
  <s xml:id="echoid-s2027" xml:space="preserve">Tandem <emph style="sc">Nicolavs</emph> <lb/><emph style="sc">Voigtel</emph>, Decumanus Iſlebienſis, et artis antea laudatae ſcien-<lb/>tiſſimus, libro germanico de geometria ſubterranea primum, Iſ le-<lb/>biae a. </s>
  <s xml:id="echoid-s2028" xml:space="preserve">1686. </s>
  <s xml:id="echoid-s2029" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2030" xml:space="preserve">deinde a. </s>
  <s xml:id="echoid-s2031" xml:space="preserve">1713. </s>
  <s xml:id="echoid-s2032" xml:space="preserve">iterum publicato, copioſius luculen-<lb/>tiusque ſcripſit, et de hoc argumento praeclare eſt meritus. </s>
  <s xml:id="echoid-s2033" xml:space="preserve">Celeb. </s>
  <s xml:id="echoid-s2034" xml:space="preserve"><lb/>L. </s>
  <s xml:id="echoid-s2035" xml:space="preserve">C. </s>
  <s xml:id="echoid-s2036" xml:space="preserve"><emph style="sc">Stvrmivs</emph> in appendice compendii mathematici <lb/>german. </s>
  <s xml:id="echoid-s2037" xml:space="preserve">quae de polygonis regularibus, circino proportionali, tri-<lb/>gonometria plana, inprimis praecipit, etiam quarto loco p. </s>
  <s xml:id="echoid-s2038" xml:space="preserve">44. </s>
  <s xml:id="echoid-s2039" xml:space="preserve">edit. </s>
  <s xml:id="echoid-s2040" xml:space="preserve"><lb/>Francof. </s>
  <s xml:id="echoid-s2041" xml:space="preserve">ad Oder. </s>
  <s xml:id="echoid-s2042" xml:space="preserve">1710. </s>
  <s xml:id="echoid-s2043" xml:space="preserve">de geometria ſubterranea nonnulla dixit, <lb/>uerum intra prima illius artis rudimenta eidem placuit ſubſiſtere.</s>
  <s xml:id="echoid-s2044" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div37" type="section" level="1" n="25">
<head xml:id="echoid-head42" xml:space="preserve">DEFINITIO III.</head>
<p>
  <s xml:id="echoid-s2045" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2046" xml:space="preserve">In triangulo rectangulo A B C, A B cathetus, germ. <lb/></s>
  <s xml:id="echoid-s2047" xml:space="preserve">
<anchor type="note" xlink:label="note-0122-01a" xlink:href="note-0122-01"/>
Seigere - Teuſſe, B C, baſis, g. </s>
  <s xml:id="echoid-s2048" xml:space="preserve">Sohle, A C hypotenuſa <lb/>germ. </s>
  <s xml:id="echoid-s2049" xml:space="preserve">die Flaeche uocatur.</s>
  <s xml:id="echoid-s2050" xml:space="preserve"/>
</p>
<div xml:id="echoid-div37" type="float" level="2" n="1">
<note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">Figur. 2.</note>
</div>
</div>
<div xml:id="echoid-div39" type="section" level="1" n="26">
<head xml:id="echoid-head43" xml:space="preserve">DEFINITIO IV.</head>
<p>
  <s xml:id="echoid-s2051" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2052" xml:space="preserve">Horae, Stunden, ſunt partes uigeſimae quartae circuli, <lb/>qui in pyxide acum magneticam cingit. </s>
  <s xml:id="echoid-s2053" xml:space="preserve">Et quaelibet <lb/>pars horaria iterum in octo aequales diuiditur.</s>
  <s xml:id="echoid-s2054" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div40" type="section" level="1" n="27">
<head xml:id="echoid-head44" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s2055" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2056" xml:space="preserve">Quamobrem autem mutauerint menſores diuiſionem circuli <lb/>communem et peruetuſtam in gradus 360, quippe quae iam
<pb o="7" file="0123" n="128" rhead="GEOMETRIA SVBTERRANEA."/>
dudum <emph style="sc">Ptolemaeo</emph> Magn. </s>
  <s xml:id="echoid-s2057" xml:space="preserve">Compoſ. </s>
  <s xml:id="echoid-s2058" xml:space="preserve">l. </s>
  <s xml:id="echoid-s2059" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2060" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2061" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2062" xml:space="preserve">placuit, et <lb/>quare in eius locum ſectionem in particulas 192 receperint, illius <lb/>rei non incongruam uidentur rationem reddere, qui ſuſpicantur, <lb/>ideo id fuiſſe factum, quia in paruo circulo, cuius diameter eſt 2 <lb/>vel 2 {1/2} digitorum, partes trecenteſimae et ſexageſimae nimis <lb/>euadunt minutae, ut non ſatis accurate ab apice acus monſtrentur, <lb/>partes uero octauae horarum, in exiguo eiusmodi ambitu, paulo <lb/>magis conſpicuae ſunt, ut in tenebris cryptarum candelae lumi-<lb/>ne ſatis illuſtrari poſſint. </s>
  <s xml:id="echoid-s2063" xml:space="preserve">Interim recepta illa diuiſione minutorum <lb/>192 conſtat, ſemicirculum 96, et quadrantem 48 particulas <lb/>continere.</s>
  <s xml:id="echoid-s2064" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div41" type="section" level="1" n="28">
<head xml:id="echoid-head45" xml:space="preserve">DEFINITIO V.</head>
<p>
  <s xml:id="echoid-s2065" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2066" xml:space="preserve">Singulae horae ſex, cuiuis quadranti debitae, a plaga <lb/>proxima nomen habent. </s>
  <s xml:id="echoid-s2067" xml:space="preserve">Ita circa meridianam utrim-<lb/>que poſitae horae 12 - 3 et 9 - 12, dicuntur meridionales, <lb/>uel ſeptentrionales; </s>
  <s xml:id="echoid-s2068" xml:space="preserve">quae autem ſunt prope puncta orientis <lb/>et occidentis utrimque collocatae, a 3 - 6 et 6 - 9, orientales <lb/>et occidentales nominantur.</s>
  <s xml:id="echoid-s2069" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div42" type="section" level="1" n="29">
<head xml:id="echoid-head46" xml:space="preserve">DEFINITIO VI.</head>
<p>
  <s xml:id="echoid-s2070" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2071" xml:space="preserve">Cauerna perpendicularis A B a ſummo ad cryptas demiſſa, <lb/>
<anchor type="note" xlink:label="note-0123-01a" xlink:href="note-0123-01"/>
per quam eo deſcenditur, uel aer admittitur, vel <lb/>metalla extrahuntur, inpoſterum puteus, germ. </s>
  <s xml:id="echoid-s2072" xml:space="preserve">ein Schacht, <lb/>dicetur. </s>
  <s xml:id="echoid-s2073" xml:space="preserve">Eius amplitudo differt, prouti uel ſoli deſcenſui <lb/>deſtinatur, uel una extrahendis ex cauerna metallis et <lb/>lapidibus, machina nempe tractoria ſuper eum ſtatuta, <lb/>aptatur. </s>
  <s xml:id="echoid-s2074" xml:space="preserve">priore caſu, perticae metallicae dimidiae latus <lb/>ſufficit, altero caſu, latitudo dimidiae perticae ſeruatur, <lb/>et longuitudini pertica una additur.</s>
  <s xml:id="echoid-s2075" xml:space="preserve"/>
</p>
<div xml:id="echoid-div42" type="float" level="2" n="1">
<note position="right" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">Figur. 1.</note>
</div>
</div>
<div xml:id="echoid-div44" type="section" level="1" n="30">
<head xml:id="echoid-head47" xml:space="preserve">DEFINITIO VII.</head>
<p>
  <s xml:id="echoid-s2076" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2077" xml:space="preserve">Cryptarum vel ſpecuum (Gruben) nomine generali in <lb/>poſterum ſignificabimus caua ſubter terram facta.</s>
  <s xml:id="echoid-s2078" xml:space="preserve">
<pb o="8" file="0124" n="129" rhead="GEOMETRIA SVBTERRANEA."/>
Appellationes reliquas, germanis praeſertim uſitatas, ono-<lb/>maſticorum ſcriptores deinceps laudandi exponunt.</s>
  <s xml:id="echoid-s2079" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div45" type="section" level="1" n="31">
<head xml:id="echoid-head48" xml:space="preserve">DEFINITIO VIII.</head>
<p>
  <s xml:id="echoid-s2080" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2081" xml:space="preserve">Inter cryptas inprimis memorabilis, et peculiaribus quo-<lb/>que iuribus a reliquis ſecreta eſt, quam Cuniculum (Stolln) <lb/>dicunt. </s>
  <s xml:id="echoid-s2082" xml:space="preserve">Qui nempe horizontali fere ductu, per unam plu-<lb/>reſue fodinarum regiones, (Sympoſia, Zechen) agitur, <lb/>ut per eum ad fodinas aeris liberi circulus producatur, <lb/>halitusque foſſoribus noxii auertantur, et aquae etiam <lb/>undiquaque ex terra prorumpentes, collectaeque, in proxi-<lb/>mas ualles deriuentur.</s>
  <s xml:id="echoid-s2083" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div46" type="section" level="1" n="32">
<head xml:id="echoid-head49" xml:space="preserve">DEFINITIO IX.</head>
<p>
  <s xml:id="echoid-s2084" xml:space="preserve">12. </s>
  <s xml:id="echoid-s2085" xml:space="preserve">Situs ſpecuum, tum qua obliquitatem ad horizontem, <lb/>ſiue lineam horizontalem, tum qua partes uel plagas <lb/>mundi, ſpectari poteſt. </s>
  <s xml:id="echoid-s2086" xml:space="preserve">De poſteriore, ſuo loco agetur. <lb/></s>
  <s xml:id="echoid-s2087" xml:space="preserve">Quoad primum uero, hic explicanda eſt diuiſio crypta-<lb/>rum in ſurgentes uel aſcendentes, (ſteigende) &amp; </s>
  <s xml:id="echoid-s2088" xml:space="preserve">in cadentes. </s>
  <s xml:id="echoid-s2089" xml:space="preserve"><lb/>(ſallende) illae ſunt, quae ſupra horizontalem, in qua <lb/>obſeruatio inſtituitur, ad uerticem attolluntur, ſiue, in <lb/>quibus filum, ex quo pondus in libella dependet, ante <lb/>normalem cadit. </s>
  <s xml:id="echoid-s2090" xml:space="preserve">Cadentes ſunt, quae infra horizonta-<lb/>lem, in qua fit obſeruatio, inclinantur, ſiue, in quibus <lb/>filum libellae a pondere ſuo poſt normalem trahitur. </s>
  <s xml:id="echoid-s2091" xml:space="preserve"><lb/>Obliquitas fodinarum uocatur germanis menſoribus die <lb/>Donlege.</s>
  <s xml:id="echoid-s2092" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div47" type="section" level="1" n="33">
<head xml:id="echoid-head50" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2093" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2094" xml:space="preserve">Haec de ſurgentibus uel cadentibus fodinis obſeruatio <lb/>omnino ad mutuam proximarum poſitionem pertinet. <lb/></s>
  <s xml:id="echoid-s2095" xml:space="preserve">Nam dum deſcendit menſor per cauernam inclinatam, caſum <lb/>eius notare debet, ſi uero ex imo ſurſum pergendo menſuras <lb/>caperet, fieret aſcendenti ſurgens fodina, quae deſcendenti <lb/>cadens erat. </s>
  <s xml:id="echoid-s2096" xml:space="preserve">Quamobrem ad locum, ubi inclinationes no-<lb/>tantur, reſtrictas uolui definitiones. </s>
  <s xml:id="echoid-s2097" xml:space="preserve">Praeterea cum eleuatio-
<pb o="9" file="0125" n="130" rhead="GEOMETRIA SVBTERRANEA."/>
nes uel caſus ſpecuum perpendiculis aeſtimentur, apparet, <lb/>pro eadem hypotenuſa ſimiles eſſe cathetos aſcenſus uel <lb/>caſus. </s>
  <s xml:id="echoid-s2098" xml:space="preserve">de quo inferius dicendi locus erit.</s>
  <s xml:id="echoid-s2099" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div48" type="section" level="1" n="34">
<head xml:id="echoid-head51" xml:space="preserve">DEFINITIO X.</head>
<p>
  <s xml:id="echoid-s2100" xml:space="preserve">14. </s>
  <s xml:id="echoid-s2101" xml:space="preserve">Loci uocabulum uarias penes metallarios ſigniſicati-<lb/>ones habet. </s>
  <s xml:id="echoid-s2102" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2103" xml:space="preserve">Locus (Orth) notat extremum fodinae, <lb/>quousque porrectum eſt. </s>
  <s xml:id="echoid-s2104" xml:space="preserve">Et hoc ſpeciatim locum termina-<lb/>tum (ganiz Orth) nominant. </s>
  <s xml:id="echoid-s2105" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2106" xml:space="preserve">Loca (Oerthumgen) finitori-<lb/>bus ſunt quaeuis definita fodinarum puncta, nonnunquam <lb/>etiam ſignis v. </s>
  <s xml:id="echoid-s2107" xml:space="preserve">g crucis, lapidi inſculptis diſtincta. </s>
  <s xml:id="echoid-s2108" xml:space="preserve">Qui-<lb/>bus quando reſpondentia in externa terrae ſuperficie mon-<lb/>ſtrantur, praxin talem artifices uocant, Oerthung an Tag <lb/>ausbringen. </s>
  <s xml:id="echoid-s2109" xml:space="preserve">Et palus pro loco ſignando poſitus, localis, Orth-<lb/>pflock, Orth - Pfahl, lapis uero terminalis, in extremo areae, <lb/>uel ſoli ad fodinam relati, der Loch-Stein, germanis dicitur.</s>
  <s xml:id="echoid-s2110" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div49" type="section" level="1" n="35">
<head xml:id="echoid-head52" xml:space="preserve">SCHOLION.</head>
<p>
  <s xml:id="echoid-s2111" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2112" xml:space="preserve">Haec de praecipuis nominibus, ad inſtitutum noſtrum inprimis <lb/>ſpectantibus, praemonenda erant. </s>
  <s xml:id="echoid-s2113" xml:space="preserve">Reliqua uocabula technica <lb/>metallifoſſoribus uſitata, iam olim prolixe enumer auit, et latine uer-<lb/>tit <emph style="sc">Georgivs</emph> <emph style="sc">Agricola</emph>, ſub finem operis de Re Metallica. <lb/></s>
  <s xml:id="echoid-s2114" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2115" xml:space="preserve">539. </s>
  <s xml:id="echoid-s2116" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2117" xml:space="preserve">praeterea eadem peculiari indice alphabetico explicata <lb/>occurrunt, in A<emph style="sc">BR.</emph> a <emph style="sc">Schönberg</emph> Berg - Information ed. </s>
  <s xml:id="echoid-s2118" xml:space="preserve"><lb/>Lipſiae. </s>
  <s xml:id="echoid-s2119" xml:space="preserve">1693. </s>
  <s xml:id="echoid-s2120" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2121" xml:space="preserve">B. </s>
  <s xml:id="echoid-s2122" xml:space="preserve">G. </s>
  <s xml:id="echoid-s2123" xml:space="preserve">C. </s>
  <s xml:id="echoid-s2124" xml:space="preserve"><emph style="sc">Kirchmaieri</emph> Inſtitutionibus Me-<lb/>tallicis, Vitemb. </s>
  <s xml:id="echoid-s2125" xml:space="preserve">a 1687. </s>
  <s xml:id="echoid-s2126" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2127" xml:space="preserve"><emph style="sc">Christiani</emph> <emph style="sc">Berwardi</emph> Lexi-<lb/>co peculiari Ff. </s>
  <s xml:id="echoid-s2128" xml:space="preserve">1684. </s>
  <s xml:id="echoid-s2129" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2130" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s2131" xml:space="preserve">item in A<emph style="sc">NON.</emph> Neueröfneten <lb/>Bergwerck. </s>
  <s xml:id="echoid-s2132" xml:space="preserve">qui tractatus inſertus eſt Part. </s>
  <s xml:id="echoid-s2133" xml:space="preserve">III. </s>
  <s xml:id="echoid-s2134" xml:space="preserve">des geöffneten <lb/>Ritterplatzes. </s>
  <s xml:id="echoid-s2135" xml:space="preserve">Num. </s>
  <s xml:id="echoid-s2136" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2137" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2138" xml:space="preserve">127. </s>
  <s xml:id="echoid-s2139" xml:space="preserve">add. </s>
  <s xml:id="echoid-s2140" xml:space="preserve">D. </s>
  <s xml:id="echoid-s2141" xml:space="preserve"><emph style="sc">Christoph</emph> <emph style="sc">Hertwig</emph> <lb/>vollkommenes Bergbuch. </s>
  <s xml:id="echoid-s2142" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s2143" xml:space="preserve">Dreſdae. </s>
  <s xml:id="echoid-s2144" xml:space="preserve">1710, f. </s>
  <s xml:id="echoid-s2145" xml:space="preserve">et 10. </s>
  <s xml:id="echoid-s2146" xml:space="preserve"><emph style="sc">Chri-</emph> <lb/><emph style="sc">STOPH</emph> <emph style="sc">Nehring</emph> Lexicon politicum. </s>
  <s xml:id="echoid-s2147" xml:space="preserve">Append. </s>
  <s xml:id="echoid-s2148" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2149" xml:space="preserve">von Berg-<lb/>wercks - Terminis. </s>
  <s xml:id="echoid-s2150" xml:space="preserve">Supereſt, ut inſtrumentorum neceſſariorum <lb/>deſcriptionem afferam.</s>
  <s xml:id="echoid-s2151" xml:space="preserve"/>
</p>
<pb o="10" file="0126" n="131" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div50" type="section" level="1" n="36">
<head xml:id="echoid-head53" xml:space="preserve">DEFINITIO XI.</head>
<p>
  <s xml:id="echoid-s2152" xml:space="preserve">16. </s>
  <s xml:id="echoid-s2153" xml:space="preserve">Menſura, finitoribus metallicis uſitata, eſt pertica <lb/>breuior, quam ulnam ſiue orgyiam nominabimus, <lb/>quia lineae, quae inter manus expanſas continetur, fere <lb/>aequalis eſt. </s>
  <s xml:id="echoid-s2154" xml:space="preserve">Germanice Lachter. </s>
  <s xml:id="echoid-s2155" xml:space="preserve">(G<emph style="sc">EORG.</emph> <emph style="sc">Agricola</emph>, <lb/>de re metall. </s>
  <s xml:id="echoid-s2156" xml:space="preserve">L. </s>
  <s xml:id="echoid-s2157" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2158" xml:space="preserve">pasſum uocat.) </s>
  <s xml:id="echoid-s2159" xml:space="preserve">Haec ulna in octo par-<lb/>tes quaſi totidem pedes diuiditur. </s>
  <s xml:id="echoid-s2160" xml:space="preserve">Octaua pars deca-<lb/>dem digitorum capit, qua ratione ulna 80. </s>
  <s xml:id="echoid-s2161" xml:space="preserve">digitos <lb/>complectitur. </s>
  <s xml:id="echoid-s2162" xml:space="preserve">Digitus uero iterum in 10. </s>
  <s xml:id="echoid-s2163" xml:space="preserve">lineas uel <lb/>ſcrupulos ſecatur, atque ita ulna menſorum capit 800. <lb/></s>
  <s xml:id="echoid-s2164" xml:space="preserve">lineas uel minuta, eidemque proportioni etiam tabulae <lb/>accommodatae ſunt. </s>
  <s xml:id="echoid-s2165" xml:space="preserve">Longitudo huius perticae non ubi-<lb/>uis eadem eſt; </s>
  <s xml:id="echoid-s2166" xml:space="preserve">Freibergae capit 3 {1/2}. </s>
  <s xml:id="echoid-s2167" xml:space="preserve">ulnas breues, ſiue cubi-<lb/>tos Dreſdenſes, et ſi Freibergenſi tribuantur partes 500. </s>
  <s xml:id="echoid-s2168" xml:space="preserve"><lb/>Ioachimthalenſis habet ſimiles minutias 493. </s>
  <s xml:id="echoid-s2169" xml:space="preserve">Iſlebienſis 507. </s>
  <s xml:id="echoid-s2170" xml:space="preserve"><lb/>Clausthalenſis 485. </s>
  <s xml:id="echoid-s2171" xml:space="preserve">complectitur.</s>
  <s xml:id="echoid-s2172" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div51" type="section" level="1" n="37">
<head xml:id="echoid-head54" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2173" xml:space="preserve">17. </s>
  <s xml:id="echoid-s2174" xml:space="preserve"><emph style="sc">Voigtel</emph> ſub principium libri ſui, doctrinae cauſa, et ob <lb/>facilitatem calculi decimalis, ulnam in 10. </s>
  <s xml:id="echoid-s2175" xml:space="preserve">partes ſecuit, deci-<lb/>mam in 10. </s>
  <s xml:id="echoid-s2176" xml:space="preserve">alias diuidi uoluit, partes eiusmodi decimales ipſi ueniunt <lb/>nomine ſcrupulorum, primorum, ſecundorum, tertiorum iisdemque <lb/>quibus geometrae perticam, pedes, digitos et grana notant, chara-<lb/>cteribus 0. </s>
  <s xml:id="echoid-s2177" xml:space="preserve">I. </s>
  <s xml:id="echoid-s2178" xml:space="preserve">II. </s>
  <s xml:id="echoid-s2179" xml:space="preserve">III. </s>
  <s xml:id="echoid-s2180" xml:space="preserve">ſignificantur. </s>
  <s xml:id="echoid-s2181" xml:space="preserve">Verum nondum illa methodus, <lb/>in ſe licet laudatiſſima et perfectiſſima, omnibus ſeſe probauit, quare <lb/>uſitatam diuiſionem retinere, et t@bulas quoque illi conformare malui.</s>
  <s xml:id="echoid-s2182" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div52" type="section" level="1" n="38">
<head xml:id="echoid-head55" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2183" xml:space="preserve">18. </s>
  <s xml:id="echoid-s2184" xml:space="preserve">Cum magnitudo ulnae fosſorum fere aequalis ſit menſurae <lb/>molitorum, ſummus aliquis et r@rum metallicarum peri-<lb/>tiſſimus uir ſuſpicatur, quod forſan hi primi metallis in miſniae <lb/>montibus indagandis operam dederint, uel ſaltem regendis eius-<lb/>modi laboribus adhibiti fuerint, tanquam gnari artificiorum, qui-
<pb o="11" file="0127" n="132" rhead="GEOMETRIA SVBTERRANEA."/>
bus aquae opportune deriuantur, et machinamenta uaria componun-<lb/>tur. </s>
  <s xml:id="echoid-s2185" xml:space="preserve">Hanc menſuram metallicam <emph style="sc">Georgivs</emph> <emph style="sc">Agricola</emph> de <lb/>re metall. </s>
  <s xml:id="echoid-s2186" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2187" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2188" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2189" xml:space="preserve">55. </s>
  <s xml:id="echoid-s2190" xml:space="preserve">ex graecorum conſuetudine ad germanos deflu-<lb/>xiſſe arbitratur, quia pes metallicus prope accedit ad longitudinem <lb/>pedis graeci.</s>
  <s xml:id="echoid-s2191" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div53" type="section" level="1" n="39">
<head xml:id="echoid-head56" xml:space="preserve">SCHOLION III.</head>
<p style="it">
  <s xml:id="echoid-s2192" xml:space="preserve">19. </s>
  <s xml:id="echoid-s2193" xml:space="preserve">Vt ulna metiendis cryptis recte applicetur, definitur tenuibus <lb/>filis aeneis connexis, praeterea tamen filum cannabinum, ſpiſſi-<lb/>tudinem caulis pennae habens, in quo ulnae aliquot lamellis cu-<lb/>preis appenſis numerantur, ad manus eſſe debet, ut tum extra <lb/>fodinas ſerena tempeſtate menſio eodem ſuſcipiatur, et in fodinis quo-<lb/>que idem extendatur. </s>
  <s xml:id="echoid-s2194" xml:space="preserve">Intra terram uero, utpote ubi plerumque <lb/>humidus aer eſt, filum tale ſaltem inueniendae cryptarum directi-<lb/>oni ſeruit, longitudo linearum capiendarum ulna orichalcea uel <lb/>lignea menſuratur, nam funiculi humoribus imbuti repente con-<lb/>trahuntur. </s>
  <s xml:id="echoid-s2195" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2196" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2197" xml:space="preserve">Aerometr.)</s>
  <s xml:id="echoid-s2198" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div54" type="section" level="1" n="40">
<head xml:id="echoid-head57" xml:space="preserve">SCHOLION IV.</head>
<p style="it">
  <s xml:id="echoid-s2199" xml:space="preserve">20. </s>
  <s xml:id="echoid-s2200" xml:space="preserve">Vtile etiam eſt, afferre in fodinas, quatuor uel ſex cochleas <lb/>aereas, capulis ligneis inſtructas, quibus tanquam terebris <lb/>funiculus tenſus firmari locis conuenientibus queat. </s>
  <s xml:id="echoid-s2201" xml:space="preserve">Figura O coch-<lb/>
<anchor type="note" xlink:label="note-0127-01a" xlink:href="note-0127-01"/>
leae imaginem ob oculos ponit.</s>
  <s xml:id="echoid-s2202" xml:space="preserve"/>
</p>
<div xml:id="echoid-div54" type="float" level="2" n="1">
<note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">Tab. 1.</note>
</div>
</div>
<div xml:id="echoid-div56" type="section" level="1" n="41">
<head xml:id="echoid-head58" xml:space="preserve">DEFINITIO XII.</head>
<p>
  <s xml:id="echoid-s2203" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2204" xml:space="preserve">Libella, Waſſer-Waage, Grad-Bogen, eſt ſemicirculus ex <lb/>
<anchor type="note" xlink:label="note-0127-02a" xlink:href="note-0127-02"/>
tenui orichalci lamella paratus, in ſingulos gradus <lb/>integros et dimidios diuiſus, uncinulis conuerſis, et pon-<lb/>dere ex filo in centro firmato penſili inſtructus, diametrum <lb/>habens 6 digitorum.</s>
  <s xml:id="echoid-s2205" xml:space="preserve"/>
</p>
<div xml:id="echoid-div56" type="float" level="2" n="1">
<note position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">Figur. 3.</note>
</div>
</div>
<div xml:id="echoid-div58" type="section" level="1" n="42">
<head xml:id="echoid-head59" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2206" xml:space="preserve">22. </s>
  <s xml:id="echoid-s2207" xml:space="preserve">Compoſitio libellae ex Figur 3. </s>
  <s xml:id="echoid-s2208" xml:space="preserve">perſpicua eſt, opera modo detur, <lb/>ut gradus accurate diuidantur, et ut leue ſit organon, ne
<pb o="12" file="0128" n="133" rhead="GEOMETRIA SVBTERRANEA."/>
funiculum oneret aut incuruet: </s>
  <s xml:id="echoid-s2209" xml:space="preserve">unci libellae et compaſſi penſilis uel in <lb/>unam partem, uel reciproce, alter prorſum, alter retrorſum cur-<lb/>uantur. </s>
  <s xml:id="echoid-s2210" xml:space="preserve">Nec abs re erit, pro uncis formandis laminas arctius com-<lb/>primere, ut elaterio quodam inſtructae etiam funiculum, quem <lb/>ambiunt, tenacius complectantur, et ut eo, quo ſuſpenſa ſunt organa <lb/>loco, conſtanter haereant. </s>
  <s xml:id="echoid-s2211" xml:space="preserve">Magis tamen haec obſeruatio ad com-<lb/>paſſum penſilem, quam ad libellam, ſpectat. </s>
  <s xml:id="echoid-s2212" xml:space="preserve">Nam in hac liberi et <lb/>aperti unci ſint oportet, quia comprimendo uel dilatando facile <lb/>immutatur paralleliſmus diametri et funiculi, intra uncos libellae <lb/>extenſi. </s>
  <s xml:id="echoid-s2213" xml:space="preserve">Situ autem illo immutato, angulorum indicatio fallit.</s>
  <s xml:id="echoid-s2214" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div59" type="section" level="1" n="43">
<head xml:id="echoid-head60" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2215" xml:space="preserve">23. </s>
  <s xml:id="echoid-s2216" xml:space="preserve">Pro imitandis, qui libella reperti ſunt, angulis, tranſportato-<lb/>rium, quod a uulgari non differt, adhibetur.</s>
  <s xml:id="echoid-s2217" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div60" type="section" level="1" n="44">
<head xml:id="echoid-head61" xml:space="preserve">SCHOLION III.</head>
<p style="it">
  <s xml:id="echoid-s2218" xml:space="preserve">24. </s>
  <s xml:id="echoid-s2219" xml:space="preserve">Vſus etiam eſt frequens ponderis ſolitarii, quod perpendicu-<lb/>lum uocant, quod ex filo ſuſpenſum, ad puteorum altitudi-<lb/>nes metiendas ualet.</s>
  <s xml:id="echoid-s2220" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div61" type="section" level="1" n="45">
<head xml:id="echoid-head62" xml:space="preserve">DEFINITIO XIII.</head>
<p>
  <s xml:id="echoid-s2221" xml:space="preserve">25. </s>
  <s xml:id="echoid-s2222" xml:space="preserve">Compaſſus penſilis (der Heng-Gruben - order Berg-Compaſſ.) <lb/></s>
  <s xml:id="echoid-s2223" xml:space="preserve">
<anchor type="note" xlink:label="note-0128-01a" xlink:href="note-0128-01"/>
eſt annulus aeneus latior ECFD, uncis A et B, <lb/>alioque annulo graciliore CGD, tranſuerſe in medio <lb/>prioris poſito, praeditus. </s>
  <s xml:id="echoid-s2224" xml:space="preserve">Intra duos hoſce annulos ex <lb/>axibus, qui foraminibus in graciliore annulo exiſtentibus, <lb/>inſeruntur, ſuſpenditur arcula, uel pyxis KH, in qua <lb/>acus magnetica ſtilo acumiſiato impoſita iacet. </s>
  <s xml:id="echoid-s2225" xml:space="preserve">Diame-<lb/>ter pyxidis eſt duorum cum dimidio uel trium digitorum. <lb/></s>
  <s xml:id="echoid-s2226" xml:space="preserve">In fundo eiusdem circa acus fulcrum circuli periphe-<lb/>ria deſcribitur, et in partes ſiue horas XXIV, quarum <lb/>quaelibet iterum octo minutias capit, ſecatur. </s>
  <s xml:id="echoid-s2227" xml:space="preserve">Plagae <lb/>autem orientis et occidentis inuerſe ſcribuntur, nempe <lb/>ubi in uulgaribus compaſſis occidens ponitur, ibi in <lb/>compaſſo metallico oriens collocatur.</s>
  <s xml:id="echoid-s2228" xml:space="preserve"/>
</p>
<div xml:id="echoid-div61" type="float" level="2" n="1">
<note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">Figur 4.</note>
</div>
<pb o="13" file="0129" n="134" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div63" type="section" level="1" n="46">
<head xml:id="echoid-head63" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2229" xml:space="preserve">26. </s>
  <s xml:id="echoid-s2230" xml:space="preserve">Cum itaque in annulo tranſuerſario, pyxis circa axes <lb/>ſuos facile mobilis, et praeterea utraque parte aequa-<lb/>liter librata ſit, ſeruabit ea ſemper ſitum horizonti parallelum, <lb/>etiamſi compaſſus ex funiculo obliquo inclinatoque ad hori-<lb/>zontalem pendeat: </s>
  <s xml:id="echoid-s2231" xml:space="preserve">Quam uirtutem huius inſtrumenti non <lb/>poſtremam eſſe, ex pragmatia, cui applicatur, uberius <lb/>mtelligetur.</s>
  <s xml:id="echoid-s2232" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div64" type="section" level="1" n="47">
<head xml:id="echoid-head64" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2233" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2234" xml:space="preserve">Vtar, lectoris uenia, uocabulo compaſſi nouo, quia inſtrumentum <lb/>ipſum nouum eſt, ueteribus, quantum conſtat, ignoratum, <lb/>alias potuiſſem amuſſium cum <emph style="sc">Vitrvvio</emph> uocare, cuius beneficio <lb/>plagarum mundi ſitus inueſtigabatur. </s>
  <s xml:id="echoid-s2235" xml:space="preserve">Nec ineptum eſſet nomen <lb/>uorſoriae uel uerſoriae, quod legitur in <emph style="sc">Plavti</emph> Mercatore <lb/>Act. </s>
  <s xml:id="echoid-s2236" xml:space="preserve">5 Scen. </s>
  <s xml:id="echoid-s2237" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2238" xml:space="preserve">v. </s>
  <s xml:id="echoid-s2239" xml:space="preserve">34. </s>
  <s xml:id="echoid-s2240" xml:space="preserve">inquit etiam, huc ſecundus uentus eſt, cape <lb/>modo uorſoriam. </s>
  <s xml:id="echoid-s2241" xml:space="preserve">Siquidem ibi inſtrumentum nauticum, temo-<lb/>nem ſcilicet aut funiculum, cuius beneficio nauis uelumue ſecundum <lb/>auram uertebatur, ſigniſicari, uix uidetur dubitandum. </s>
  <s xml:id="echoid-s2242" xml:space="preserve">Sed diſpa-<lb/>rilis tamen magneticae acus utilitas eſt, quapropter nouum notiſſi-<lb/>mumque nomen merito retinetur. </s>
  <s xml:id="echoid-s2243" xml:space="preserve"><emph style="sc">Agricola</emph> ſub finem operis <lb/>de re metall. </s>
  <s xml:id="echoid-s2244" xml:space="preserve">compaſſum uocat inſtrumentum metallicum, ſignificans <lb/>mundi partis. </s>
  <s xml:id="echoid-s2245" xml:space="preserve">Quae appellatio et longa nimis eſt, et diſcrimina compaſſi <lb/>penſilis et iacentis non indicat. </s>
  <s xml:id="echoid-s2246" xml:space="preserve">Et forſan compaſſi penſilis inuen-<lb/>tum aetate <emph style="sc">Agricolae</emph> poſterius eſt. </s>
  <s xml:id="echoid-s2247" xml:space="preserve">Siquidem libro 5. </s>
  <s xml:id="echoid-s2248" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2249" xml:space="preserve">104. <lb/></s>
  <s xml:id="echoid-s2250" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2251" xml:space="preserve">ubi menſorum organa deſcribit, tantum praeter libram, pyxidis <lb/>magneticae iacentis facit mentionem. </s>
  <s xml:id="echoid-s2252" xml:space="preserve">Qua in opinione, poſtquam <lb/><emph style="sc">Reinholdi</emph> librum euolui, in quo compaſſus quoque tantum iacens <lb/>laudatur, magis magisqne confirmor. </s>
  <s xml:id="echoid-s2253" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2254" xml:space="preserve">4.)</s>
  <s xml:id="echoid-s2255" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div65" type="section" level="1" n="48">
<head xml:id="echoid-head65" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2256" xml:space="preserve">28. </s>
  <s xml:id="echoid-s2257" xml:space="preserve">Spectat hoc inſtrumentum ad commode inueniendum fodinarum <lb/>ſitum, et directionem ad plagas mundi. </s>
  <s xml:id="echoid-s2258" xml:space="preserve">Inprimis uero nobis <lb/>hic explicandum uenit, quam ob cauſam contraria ratione plagas <lb/>occidentis et orientis finitores ſcribant: </s>
  <s xml:id="echoid-s2259" xml:space="preserve">Scilicet, ſuſpenditur compaſ-
<pb o="14" file="0130" n="135" rhead="GEOMETRIA SVBTERRANEA."/>
ſus ex funiculis ea lege, ut ſemper notae S et M quae ſeptemtrio-<lb/>nali et meridionali plagae adſcriptae ſunt, adeoque tota linea S M <lb/>incidant in axem, ſiue lineam directionis, ipſius fodinae, cuius po-<lb/>ſitus quaeritur. </s>
  <s xml:id="echoid-s2260" xml:space="preserve">Et continuo quidem ſignum S prorſum, ſiue in ante-<lb/>riorem partem, uertitur. </s>
  <s xml:id="echoid-s2261" xml:space="preserve">Quando igitur inuerſe ſcribuntur ſigna <lb/>Occ. </s>
  <s xml:id="echoid-s2262" xml:space="preserve">et Or. </s>
  <s xml:id="echoid-s2263" xml:space="preserve">acus magnetica, ea parte ſua, quae in ſeptentrionem reſpi-<lb/>cit, monſtrat plagam, in quam fodina porrigitur. </s>
  <s xml:id="echoid-s2264" xml:space="preserve">Ingenioſe autem <lb/>compaſſum ſuum ita compoſuere finitores, quia ipſa nunc acus certis-<lb/>ſimum et ſubtiliſſimum plagae praebet indicem. </s>
  <s xml:id="echoid-s2265" xml:space="preserve">Quantum enim linea <lb/>S M deflectit a meridiana, tantum etiam acus ab eadem recedet. <lb/></s>
  <s xml:id="echoid-s2266" xml:space="preserve">Si ergo S in occaſum collineet, acus indice ſuo ſuper Occ. </s>
  <s xml:id="echoid-s2267" xml:space="preserve">conſiſtet, <lb/>et occaſum monſtrabit, et ſimiliter in intermediis lineis ſeſe geret, <lb/>cuius conuerſae ſcriptionis effectus, uſu talis pyxidis, omnium clariſſi-<lb/>me poteſt oſtendi.</s>
  <s xml:id="echoid-s2268" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div66" type="section" level="1" n="49">
<head xml:id="echoid-head66" xml:space="preserve">DEFINITIO XIV.</head>
<p>
  <s xml:id="echoid-s2269" xml:space="preserve">29. </s>
  <s xml:id="echoid-s2270" xml:space="preserve">Inſtrumentum lineationis (das Zuleg - oder Zeichen - Inſtru-<lb/>
<anchor type="note" xlink:label="note-0130-01a" xlink:href="note-0130-01"/>
ment it. </s>
  <s xml:id="echoid-s2271" xml:space="preserve">der Zulege-Compaſ) eſt loculamentum aeneum <lb/>rectangulum, dioptras D R habens, in quo compaſſus <lb/>pendalus, ex annulo ſuo exemtus, horizontali ſitu poni et <lb/>firmari poteſt. </s>
  <s xml:id="echoid-s2272" xml:space="preserve">Linea circuli horarii S M, imponitur <lb/>lineae D R, ſuper qua dioptrae (ſeſquidigitum altae, et <lb/>circa axem mobiles, ita ut demitti, et eleuari iterum poſ-<lb/>ſint) conſiſtunt. </s>
  <s xml:id="echoid-s2273" xml:space="preserve">Longitudo organi eſt 6 uel 7 latitudo <lb/>4 digitorum; </s>
  <s xml:id="echoid-s2274" xml:space="preserve">diſtinctior eiusdem imago Fig. </s>
  <s xml:id="echoid-s2275" xml:space="preserve">V. </s>
  <s xml:id="echoid-s2276" xml:space="preserve">tab. </s>
  <s xml:id="echoid-s2277" xml:space="preserve">4. <lb/></s>
  <s xml:id="echoid-s2278" xml:space="preserve">ob oculos ponitur.</s>
  <s xml:id="echoid-s2279" xml:space="preserve"/>
</p>
<div xml:id="echoid-div66" type="float" level="2" n="1">
<note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">Fig. 5.</note>
</div>
</div>
<div xml:id="echoid-div68" type="section" level="1" n="50">
<head xml:id="echoid-head67" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2280" xml:space="preserve">30. </s>
  <s xml:id="echoid-s2281" xml:space="preserve">Vſus eius eſt, ut cluctus, compaſſo penſili inuenti, horizonta-<lb/>liter in charta delineari queant, de quo deinceps plura; </s>
  <s xml:id="echoid-s2282" xml:space="preserve">quo-<lb/>niam autem in charta, pro ducendis rectis lineis, officium facit, <lb/>commodius erit, ſi baſis ex duriore ligno u. </s>
  <s xml:id="echoid-s2283" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2284" xml:space="preserve">hebeno paretur. </s>
  <s xml:id="echoid-s2285" xml:space="preserve">Aes <lb/>enim chartam maculare ſolet.</s>
  <s xml:id="echoid-s2286" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div69" type="section" level="1" n="51">
<head xml:id="echoid-head68" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2287" xml:space="preserve">31. </s>
  <s xml:id="echoid-s2288" xml:space="preserve">Debet igitur ſolicite cum penſili compaſſo componi, ut perfectus <lb/>
<anchor type="note" xlink:label="note-0130-02a" xlink:href="note-0130-02"/>
lineae S M Fig. </s>
  <s xml:id="echoid-s2289" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2290" xml:space="preserve">et laterum AE, DR, BC, Fig. </s>
  <s xml:id="echoid-s2291" xml:space="preserve">5 obti-
<pb o="15" file="0131" n="136" rhead="GEOMETRIA SVBTERRANEA."/>
neatur paralleliſmus. </s>
  <s xml:id="echoid-s2292" xml:space="preserve">Et ne pyxis magnetica ſuum in locum repoſita <lb/>uacillet, aut facile motu inſtrumenti, a ſitu debito dimoueatur, an-<lb/>nulus aeneus elaſticus illi loculamento inſeritur, qui pyxidem ambit, <lb/>et ad eam commodius retinendam cochlea quadam premitur. </s>
  <s xml:id="echoid-s2293" xml:space="preserve">Pin-<lb/>nula organi altera aliquot parua foramina habet, reliquam partem <lb/>integra eſt. </s>
  <s xml:id="echoid-s2294" xml:space="preserve">Altera uero pinnula in medio exſecta eſt, in cuius <lb/>medio uel filum for aminibus dioptrae oppoſitae parallelum, uel <lb/>aenea lamella ſimiliter parrallela, extenditur. </s>
  <s xml:id="echoid-s2295" xml:space="preserve">Nonnulli iuxta locu-<lb/>lum pyxidis etiam horizontale horologium deſcribunt, in quo ſtili <lb/>officium filum ſericum obit, quod per pinnulae foramen ex centro <lb/>horologii ducitur. </s>
  <s xml:id="echoid-s2296" xml:space="preserve">Et tale illi, quod ego poſſideo, inſculptum eſt: <lb/></s>
  <s xml:id="echoid-s2297" xml:space="preserve">quod uſu non deſtituitur, quando menſor ſine portabili horologio <lb/>montanas regiones permetitur. </s>
  <s xml:id="echoid-s2298" xml:space="preserve">Praeterea ſic capſula fit longior, <lb/>iuxta quam dioptrae 2 {1/2} dig. </s>
  <s xml:id="echoid-s2299" xml:space="preserve">altae applicari queunt.</s>
  <s xml:id="echoid-s2300" xml:space="preserve"/>
</p>
<div xml:id="echoid-div69" type="float" level="2" n="1">
<note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">Figur. 6.</note>
</div>
</div>
<div xml:id="echoid-div71" type="section" level="1" n="52">
<head xml:id="echoid-head69" xml:space="preserve">SCHOLION III.</head>
<p style="it">
  <s xml:id="echoid-s2301" xml:space="preserve">32. </s>
  <s xml:id="echoid-s2302" xml:space="preserve">Vtriusque inſtrumenti comparatio fit ſequenti modo. </s>
  <s xml:id="echoid-s2303" xml:space="preserve">Nempe <lb/>in planitie aliqua duo ponuntur baculi, diſtantes 100 paſ-<lb/>ſibus; </s>
  <s xml:id="echoid-s2304" xml:space="preserve">alteri admouetur inſtrumentum lineationis, et per pinnulas <lb/>oppoſitus baculus reſpicitur. </s>
  <s xml:id="echoid-s2305" xml:space="preserve">Tum etiam extra pinnulas, iuxta <lb/>regularum AE, CB ductum, ſpectatur, immoto organo, idem ba-<lb/>culus, ſi utrimque baculus in linea AE, DR poſitus deprehenditur, <lb/>recte ſe habet inſtrumentum. </s>
  <s xml:id="echoid-s2306" xml:space="preserve">Siquidem ex opticis notum eſt, li-<lb/>neas parrallelas in longum productas optice concurrere. </s>
  <s xml:id="echoid-s2307" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2308" xml:space="preserve">56. </s>
  <s xml:id="echoid-s2309" xml:space="preserve">opt.) <lb/></s>
  <s xml:id="echoid-s2310" xml:space="preserve">Idem examen etiam alio exploratae perfectionis organo, parallelo <lb/>ſitu iuxta prius collocato, cognoſcitur. </s>
  <s xml:id="echoid-s2311" xml:space="preserve">Dum uero ita ſpectatur <lb/>baculus, hora ab acu indicata notatur. </s>
  <s xml:id="echoid-s2312" xml:space="preserve">Deinceps funiculus inter <lb/>duos illos baculos, uel alios intermedios in eadem linea conſtitutos, <lb/>extenditur, et compaſſus penſilis ex eo diuerſis in locis ſuſpendi-<lb/>tur, ſi acus horam eandem, quam in inſtrumento lineationis oſtende-<lb/>rat, monſtrauerit, habes utrumque organon bene conſentiens, et <lb/>antequam de conſenſu conſtet, neutrum tuto adhibetur. </s>
  <s xml:id="echoid-s2313" xml:space="preserve">add. </s>
  <s xml:id="echoid-s2314" xml:space="preserve"><lb/>V<emph style="sc">OIGTEL.</emph> p. </s>
  <s xml:id="echoid-s2315" xml:space="preserve">27.</s>
  <s xml:id="echoid-s2316" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div72" type="section" level="1" n="53">
<head xml:id="echoid-head70" xml:space="preserve">SCHOLION IV.</head>
<p style="it">
  <s xml:id="echoid-s2317" xml:space="preserve">33. </s>
  <s xml:id="echoid-s2318" xml:space="preserve">Quia menſores perpetuo acus magneticae beneficio fruuntur, <lb/>uaria circa eam obſeruarunt notatu digna, quae magnam
<pb o="16" file="0132" n="137" rhead="GEOMETRIA SVBTERRANEA."/>
partem <emph style="sc">Voigtel</emph> cum curioſis communicauit Parte 4. <lb/></s>
  <s xml:id="echoid-s2319" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2320" xml:space="preserve">30. </s>
  <s xml:id="echoid-s2321" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2322" xml:space="preserve">ex quibus nonnulla hic repetere et ſubinde illuſtrare <lb/>atque augere, operae pretium uidetur. </s>
  <s xml:id="echoid-s2323" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2324" xml:space="preserve">Nota eſt uariabilis ma-<lb/>gnetis declinatio a meridiana, quae in diuerſis locis differt, et <lb/>eodem quoque loco, interiecto aliquo temporis interuallo, mutatur. </s>
  <s xml:id="echoid-s2325" xml:space="preserve"><lb/>Vnde ſaepe linea pyxidis corrigi debet ad ductum meridianae, de <lb/>qua dixi in inſtitutionibus aſtron. </s>
  <s xml:id="echoid-s2326" xml:space="preserve">ſphaer. </s>
  <s xml:id="echoid-s2327" xml:space="preserve">§. </s>
  <s xml:id="echoid-s2328" xml:space="preserve">29. </s>
  <s xml:id="echoid-s2329" xml:space="preserve">30. </s>
  <s xml:id="echoid-s2330" xml:space="preserve">Ceterum <lb/>illud experimentum hic inprimis commemorari meretur, quo in-<lb/>notuit, declinationem acus tam eſſe inſtabilem, ut quandoque in <lb/>locis, quae duobus ſaltem milliaribus diſtant, differat, quapropter <lb/>opera danda, ut prope cauernas, in quibus anguli compaſſo capti <lb/>ſunt, inſtrumento lineationis ichnographia fodinarum abſoluatur. </s>
  <s xml:id="echoid-s2331" xml:space="preserve"><lb/>v. </s>
  <s xml:id="echoid-s2332" xml:space="preserve"><emph style="sc">Voigtel</emph> p. </s>
  <s xml:id="echoid-s2333" xml:space="preserve">113.</s>
  <s xml:id="echoid-s2334" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2335" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2336" xml:space="preserve">Impeditur uis acus magneticae frigore, quo quippe me-<lb/>talla conſtringuntur. </s>
  <s xml:id="echoid-s2337" xml:space="preserve">Quare antequam bieme in fodinas defera-<lb/>tur compaſſus, prius in conclaui calefacto temperandum frigus, et <lb/>uapor in eum incidens leniter detergendus eſt.</s>
  <s xml:id="echoid-s2338" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2339" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2340" xml:space="preserve">Curandum, ut accurate in centro figatur ſtilus, cui <lb/>acus tanquam fulcro immineat, alias enim diuerſae fient diuerſis <lb/>in arcubus graduum indicationes.</s>
  <s xml:id="echoid-s2341" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2342" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2343" xml:space="preserve">Tam fulcrum acus, quam conus uel pileolus aeneus, <lb/>in quem illud immittitur, magna induſtria poliri debent, ut eo li-<lb/>berior acui motus permittatur.</s>
  <s xml:id="echoid-s2344" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2345" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2346" xml:space="preserve">Stili cuſpis nec acuminata nec obtuſa nimis ſit. <lb/></s>
  <s xml:id="echoid-s2347" xml:space="preserve">Idem ſtilus, cochleae beneficio, intruditur, ut attolli aliquantum et <lb/>demitti acus queat.</s>
  <s xml:id="echoid-s2348" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2349" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2350" xml:space="preserve">Inter acum et uitrum, quo tegitur, ſpatium iuſtum <lb/>interſit, neceſſum eſt. </s>
  <s xml:id="echoid-s2351" xml:space="preserve">Cum autem demitur, et iterum imponitur, <lb/>pyxidi uitrum, caue ne in acum cadat, et cuſpidis acumen <lb/>obtundat.</s>
  <s xml:id="echoid-s2352" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2353" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2354" xml:space="preserve">Acus a ferro et ipſo magnete remoueatur. </s>
  <s xml:id="echoid-s2355" xml:space="preserve">Siqui-<lb/>dem utroque a ſolita directione auocatur, et ſi idem ſaepe contin-<lb/>gat, alacritas eiusdem impeditur. </s>
  <s xml:id="echoid-s2356" xml:space="preserve">Propterea etiam compaſſus in <lb/>ferrifodinis inutilis eſt.</s>
  <s xml:id="echoid-s2357" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2358" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2359" xml:space="preserve">Rudis et nondum elaborati magnetis poli ſic inueni-<lb/>untur. </s>
  <s xml:id="echoid-s2360" xml:space="preserve">Ponitur nempe aliquo loco uas rotundum, et ibidem immo-<lb/>tum relinquitur, in eoque, uel obſeruatione ſolis, quemadmodum in
<pb o="17" file="0133" n="138" rhead="GEOMETRIA SVBTERRANEA."/>
aſtronomia docetur, uel beneficio acus magneticae accuratioris, <lb/>meridianae lineae poſitus in marginis oppoſitis punctis notatur. <lb/></s>
  <s xml:id="echoid-s2361" xml:space="preserve">Tum in idem uas aqua infunditur, et aſſer leuis imponitur, aquae <lb/>innataturus, deinceps ſuper aſſere magnes locatur, et expectatur, <lb/>donec is in ſtabilem ſitum ſeſe compoſuerit, et quieuerit. </s>
  <s xml:id="echoid-s2362" xml:space="preserve">Ita enim <lb/>in ipſo, linea meridiana, in duo oppoſita marginis puncta utrim-<lb/>que reſpiciens reperitur, conf. </s>
  <s xml:id="echoid-s2363" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2364" xml:space="preserve"><emph style="sc">Mathesii</emph> S<emph style="sc">AREPTA.</emph> Conc. </s>
  <s xml:id="echoid-s2365" xml:space="preserve"><lb/>12. </s>
  <s xml:id="echoid-s2366" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2367" xml:space="preserve">129. </s>
  <s xml:id="echoid-s2368" xml:space="preserve">poſtea mola acuminaria tolluntur rudis lapidis promi-<lb/>nentiae, ita ut linea meridiana in medio relinquatur, et lapis paral-<lb/>lelepipedi figuram aſſumat. </s>
  <s xml:id="echoid-s2369" xml:space="preserve">Hinc fruſtulo magnetis exiguo lapis <lb/>paulatim admouetur, quod magnes priſmaticus, (uel ut aliis pla-<lb/>cet, ſphaericus aut elliptoidicus,) fortiter attrahet eo puncto, quo <lb/>uis omnis dirigitur et cumulatur, idemque hoc ipſo innoteſcet, ſi <lb/>ſuccutiatur magnes, et fruſtulum adhaerens aegre decidat. </s>
  <s xml:id="echoid-s2370" xml:space="preserve">Il-<lb/>lud autem punctum impreſſo charactere ſignatur, et pro polo <lb/>boreo habetur, cuius e regione altera eſt polus auſtralis, itidem <lb/>ſtilo limaue notandus. </s>
  <s xml:id="echoid-s2371" xml:space="preserve">Eadem polorum loca etiam ſic reperiuntur. </s>
  <s xml:id="echoid-s2372" xml:space="preserve"><lb/>In charta ramenta ferri ſparguntur, et ſub charta admouetur ma-<lb/>gnes priſmaticus, ſtatim enim ſcobs ferri dirigetur in duplicem <lb/>polum, et quosdam in charta arcus, et eorum ſectionis puncta, qui-<lb/>bus poli ſubiacent, determinabit. </s>
  <s xml:id="echoid-s2373" xml:space="preserve">Qualis autem alteruter polus ſit, <lb/>boreus uel auſtrinus, experieris, lapide ad acum magneticam, ſuper <lb/>fulcro ſuo mobilem, appropinquante, nam polus boreus amicam, nempe <lb/>boream acus partem, adducet, repellet inimicam. </s>
  <s xml:id="echoid-s2374" xml:space="preserve">Cognitis ſignatis-<lb/>que in lapide polis, utraque magnetis regio polaris, ferreis annulis <lb/>cingitur, et quaſi armatur, et ſuper ipſos polos, in circulis ferreis, <lb/>ferra prominentia et polita figuntur, poſtea armatus magnes linteo <lb/>uel ſerico panno ueſtitur. </s>
  <s xml:id="echoid-s2375" xml:space="preserve">conf. </s>
  <s xml:id="echoid-s2376" xml:space="preserve">V<emph style="sc">OIGTEL.</emph> l. </s>
  <s xml:id="echoid-s2377" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2378" xml:space="preserve">et <emph style="sc">Bion</emph> de inſtru-<lb/>mentis mathematicis. </s>
  <s xml:id="echoid-s2379" xml:space="preserve">L. </s>
  <s xml:id="echoid-s2380" xml:space="preserve">III. </s>
  <s xml:id="echoid-s2381" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2382" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2383" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2384" xml:space="preserve">103. </s>
  <s xml:id="echoid-s2385" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2386" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s2387" xml:space="preserve">german. </s>
  <s xml:id="echoid-s2388" xml:space="preserve">conſtat <lb/>autem experientia, armatum magnetem nudo multo potentiorem <lb/>fieri.</s>
  <s xml:id="echoid-s2389" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2390" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2391" xml:space="preserve">Aſſeruatur magnes uel in ciſtula, qua ramenta ferri con-<lb/>tinentur, uel ita ſuſpenditur, ut in mundi plagas ſeſe conuertere <lb/>poſſit, et tum ex unco ferreo, qui eiusdem armaturae adhaeret, <lb/>ferrea pondera appenduntur, quae dum ſenſim augentur, uis attra-<lb/>hendi et dirigendi in polos una incrementa capit. </s>
  <s xml:id="echoid-s2392" xml:space="preserve">Hinc autem per <lb/>ſe quisque iudicauerit, magnetem praeſtare altero tanto plus, quanto <lb/>grauior a pondera adducit.</s>
  <s xml:id="echoid-s2393" xml:space="preserve"/>
</p>
<pb o="18" file="0134" n="139" rhead="GEOMETRIA SUBTERRANEA."/>
<p style="it">
  <s xml:id="echoid-s2394" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2395" xml:space="preserve">Acus ex tenui ferri lamella facta, probe limata, et <lb/>pileolo aeneo inſtructa, facultate magnetica imbuitur, affricta <lb/>illius poli, in cuius plagam conuerti acus portio tangenda debet. <lb/></s>
  <s xml:id="echoid-s2396" xml:space="preserve">Nempe ferro polito, quod illi polo v. </s>
  <s xml:id="echoid-s2397" xml:space="preserve">g. </s>
  <s xml:id="echoid-s2398" xml:space="preserve">boreo imminet, acus alterum <lb/>brachium, a pileo uerſus finem aliquoties, quater, quinquiesue, fri-<lb/>catur, et fulcimento ſuo imponitur, ita uis directionis ſtatim ſe ex-<lb/>ſeret, et in meridiem et ſeptentrionem acum trahet. </s>
  <s xml:id="echoid-s2399" xml:space="preserve">Quidam et <lb/>alteram acus portionem polo contrario ſimiliter tangunt, uerum prae-<lb/>ter neceſſitatem.</s>
  <s xml:id="echoid-s2400" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2401" xml:space="preserve">11. </s>
  <s xml:id="echoid-s2402" xml:space="preserve">Pyxis acum complectens uitro tegitur, ut aeris flatui <lb/>non ſit obnoxia. </s>
  <s xml:id="echoid-s2403" xml:space="preserve">Inprimis autem cauendum, ne acus pinguedine et <lb/>humore, ex quo quippe ferruginem contrahit, inficiatur, neue igni <lb/>uicino exponantur, et ab iisdem magnes quoque tutus praeſtari <lb/>debet.</s>
  <s xml:id="echoid-s2404" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2405" xml:space="preserve">12. </s>
  <s xml:id="echoid-s2406" xml:space="preserve">Dum fricatur acus, ſemper in unam partem magnes <lb/>adducitur. </s>
  <s xml:id="echoid-s2407" xml:space="preserve">Nam quando reducitur, uis recto affrictu impreſſa, <lb/>inuerſo iterum tollitur.</s>
  <s xml:id="echoid-s2408" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2409" xml:space="preserve">13. </s>
  <s xml:id="echoid-s2410" xml:space="preserve">Quia acus brachium, quod tactu magnetis natiuam <lb/>ipſi indolem concepit, redditur grauius, reſtituitur ipſius aequi <lb/>librium, particula exigua abſciſſa.</s>
  <s xml:id="echoid-s2411" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2412" xml:space="preserve">14. </s>
  <s xml:id="echoid-s2413" xml:space="preserve">Cum languet acus, ſtili uel pileoli politura examinanda, <lb/>et aſperitas, ſi qua deprehenditur, lima aut ſmyride tollenda eſt. <lb/></s>
  <s xml:id="echoid-s2414" xml:space="preserve">Si ferrugo lamellam obſideat, iterum polienda eſt. </s>
  <s xml:id="echoid-s2415" xml:space="preserve">Tum denuo <lb/>magnete acus affricatur, ut uirtus priſtina reuiuiſcat.</s>
  <s xml:id="echoid-s2416" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s2417" xml:space="preserve">15. </s>
  <s xml:id="echoid-s2418" xml:space="preserve">Tandem non negligenda eſt menſorum admonitio, qua <lb/>praecipiunt, ut acus, poſt exactas pragmatias, ex compaſſo exi-<lb/>matur. </s>
  <s xml:id="echoid-s2419" xml:space="preserve">et charta inuoluta cuſtodiatur. </s>
  <s xml:id="echoid-s2420" xml:space="preserve">Siquidem quando com-<lb/>paſſus in perula obliquo ſitu collocatur, et motu ferentis concuti-<lb/>tur, contingere poteſt, ut ſtiluscet pileolus attritu mutuo ſe cor-<lb/>rumpant.</s>
  <s xml:id="echoid-s2421" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div73" type="section" level="1" n="54">
<head xml:id="echoid-head71" xml:space="preserve">DEFINITIO XV.</head>
<p>
  <s xml:id="echoid-s2422" xml:space="preserve">Goniodictes (der Winckelweiſer), eſt inſtrumentum <lb/>
<anchor type="note" xlink:label="note-0134-01a" xlink:href="note-0134-01"/>
ligneum, circiter pedis | longitudine, duabus parti-<lb/>bus AF et GH, cochlea F copulatis,@ conſtans, geſtans <lb/>praeterea dioptras aereas B, C, et infra funiculum LKI
<pb o="19" file="0135" n="140" rhead="GEOMETRIA SUBTERRANEA."/>
D, parallelum lineae dioptrarum. </s>
  <s xml:id="echoid-s2423" xml:space="preserve">Firmatur autem <lb/>ſuper fulcro, per foramen H immiſſo, et adhibetur, <lb/>tum ad linearum inclinationes ad horizontem, tum inpri-<lb/>mis ad conuerſiones uel directiones in mundi plagas, in <lb/>externa terrae ſuperficie definiendas. </s>
  <s xml:id="echoid-s2424" xml:space="preserve">Nam quando ex <lb/>funiculo HI libella ſuſpenditur, poteſt portio inſtrumenti <lb/>AE tamdiu attolli uel deprimi, donec pondus, ex cen-<lb/>tro libellae pendulum, angulum inclinationis ad horizon-<lb/>tem deſignet. </s>
  <s xml:id="echoid-s2425" xml:space="preserve">Similiter ſuſpenſo ex goniodicte compaſſo, <lb/>et moto inſtrumento dextrorſum uel ſiniſtrorſum, donec <lb/>ſub eodem acus magnetica plagam deſideratam indicet, <lb/>habetur ſitus illius in eandem mundi plagam.</s>
  <s xml:id="echoid-s2426" xml:space="preserve"/>
</p>
<div xml:id="echoid-div73" type="float" level="2" n="1">
<note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">Figur. 7. 34.</note>
</div>
</div>
<div xml:id="echoid-div75" type="section" level="1" n="55">
<head xml:id="echoid-head72" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2427" xml:space="preserve">35. </s>
  <s xml:id="echoid-s2428" xml:space="preserve">Quodſi igitur quis, obtento inſtrumenti ſitu, per dioptras <lb/>proſpiciat, poteſt in patente campo, baculis conſtitu-<lb/>tis, lineam in quodlibet horizontis punctum conuerſam de-<lb/>finire. </s>
  <s xml:id="echoid-s2429" xml:space="preserve">Ceterum ligneum eſt, ut eo euadat leuius. </s>
  <s xml:id="echoid-s2430" xml:space="preserve">Habet idem <lb/>uſum pro libellatione locorum inſtituenda; </s>
  <s xml:id="echoid-s2431" xml:space="preserve">item pro deſcri-<lb/>bendis arearum ichnographiis, ſiquidem angulos a lateribus <lb/>figurae cuiusdam comprehenſos acus indicat, qui in charta <lb/>inſtrumento lineationis accurate iterum ſiſti poſſunt. </s>
  <s xml:id="echoid-s2432" xml:space="preserve">Gonf-<lb/>dicta §. </s>
  <s xml:id="echoid-s2433" xml:space="preserve">132. </s>
  <s xml:id="echoid-s2434" xml:space="preserve">Geom. </s>
  <s xml:id="echoid-s2435" xml:space="preserve">reſol. </s>
  <s xml:id="echoid-s2436" xml:space="preserve">3.</s>
  <s xml:id="echoid-s2437" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div76" type="section" level="1" n="56">
<head xml:id="echoid-head73" xml:space="preserve">DEFINITIO XVI.</head>
<p>
  <s xml:id="echoid-s2438" xml:space="preserve">36.</s>
  <s xml:id="echoid-s2439" xml:space="preserve">Compaſſus iacens (der Setz - Compaſſ.) </s>
  <s xml:id="echoid-s2440" xml:space="preserve">eſt arcula rotunda, <lb/>
<anchor type="note" xlink:label="note-0135-01a" xlink:href="note-0135-01"/>
ex aere uel ligno parata, in cuius medio, intra caui-<lb/>tatem circularem, acus magnetica ſuper acuto ſtilo iacet, <lb/>peripheria uero in portiones ſuas horarias, quemadm o-<lb/>dum figura indicat, diuiſa eſt. </s>
  <s xml:id="echoid-s2441" xml:space="preserve">Praeterea circa pyxidem <lb/>magneticam, in medio inſertam, regula AB mobilis eſt, <lb/>cuius alterum erus uerſus A ſigno, v. </s>
  <s xml:id="echoid-s2442" xml:space="preserve">g. </s>
  <s xml:id="echoid-s2443" xml:space="preserve">crucis, ſignatur.</s>
  <s xml:id="echoid-s2444" xml:space="preserve"/>
</p>
<div xml:id="echoid-div76" type="float" level="2" n="1">
<note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">Figur. 14.</note>
</div>
<pb o="20" file="0136" n="141" rhead="GEOMETRIA SUBTERRANEA."/>
</div>
<div xml:id="echoid-div78" type="section" level="1" n="57">
<head xml:id="echoid-head74" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2445" xml:space="preserve">37. </s>
  <s xml:id="echoid-s2446" xml:space="preserve">Vſus huius inſtrumenti eſt, ut beneficio regulae mobilis <lb/>ſpecus cuiusdam directio in mundi plagam, ſiue diſceſſus <lb/>a linea meridiana, inueſtigetur, et quia in tali pyxide regula <lb/>horam alicuius cauernae axi debitam monſtrat, non opus <lb/>eſt plagarum ortus et occaſus permutatione; </s>
  <s xml:id="echoid-s2447" xml:space="preserve">adeoque hic <lb/>compaſſus ſimilis eſt uulgarium, qui circumferuntur, et tantum <lb/>diuiſione peripheriae diſtinguitur. </s>
  <s xml:id="echoid-s2448" xml:space="preserve">Aetate Agricolae, ſeculo <lb/>16, eiusmodi compaſſum prae ceteris fuiſſe in uſu, apparet ex <lb/>libro s. </s>
  <s xml:id="echoid-s2449" xml:space="preserve">eiusdem de re metallica, p. </s>
  <s xml:id="echoid-s2450" xml:space="preserve">105.</s>
  <s xml:id="echoid-s2451" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div79" type="section" level="1" n="58">
<head xml:id="echoid-head75" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s2452" xml:space="preserve">38. </s>
  <s xml:id="echoid-s2453" xml:space="preserve">Cum uero breuis acus magnetica non ſatis accurate indicet <lb/>in circulo horario punctum, finitores aliam compaſſi iacentis <lb/>formam, quae figura 15. </s>
  <s xml:id="echoid-s2454" xml:space="preserve">ob oculos ponitur, inuenerunt. </s>
  <s xml:id="echoid-s2455" xml:space="preserve">Nimirum <lb/>
<anchor type="note" xlink:label="note-0136-01a" xlink:href="note-0136-01"/>
ex ligno duriore conficitur rectangulum, 6. </s>
  <s xml:id="echoid-s2456" xml:space="preserve">digitos longum, 1. </s>
  <s xml:id="echoid-s2457" xml:space="preserve">dig. <lb/></s>
  <s xml:id="echoid-s2458" xml:space="preserve">altum, et in medio eiusdem, pro acu locanda, cauum orbiculare pa-<lb/>ratur, cuius diameter eſt 2 {1/2} digitorum. </s>
  <s xml:id="echoid-s2459" xml:space="preserve">Circa hoc cauum foramen <lb/>orbiculus aeneus tranſuerſariis diametris firmatur, in quo horarum <lb/>diuiſiones et numeri ſcripti ſunt. </s>
  <s xml:id="echoid-s2460" xml:space="preserve">In centro autem harum diametro-<lb/>rum, ſtilus figitur, intra regulae MNO medium inſerendus, <lb/>ut circa hunc ſtilum, ueluti circa axem ſuum, regula aenea, diame-<lb/>tro compaſſi panlo maior, altero extremo unco praedita, uoluatur. </s>
  <s xml:id="echoid-s2461" xml:space="preserve"><lb/>Ita enim fiet, ut etiam hoc organo reperiantur ſpecuum ſubterra-<lb/>neorum directiones, quando funiculus parietibus fodinae parallelus, <lb/>unco M regulae annexus, una ducit regulam, ut angulus, quem <lb/>cum linea meridiana funiculus efficit, innoteſcat, Si hoc inſtru-<lb/>mentum fulcro inſtruatur, erit aa praxin tanto commodius.</s>
  <s xml:id="echoid-s2462" xml:space="preserve"/>
</p>
<div xml:id="echoid-div79" type="float" level="2" n="1">
<note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">Figur 15.</note>
</div>
</div>
<div xml:id="echoid-div81" type="section" level="1" n="59">
<head xml:id="echoid-head76" xml:space="preserve">DEFINITIO XVII.</head>
<p>
  <s xml:id="echoid-s2463" xml:space="preserve">39.</s>
  <s xml:id="echoid-s2464" xml:space="preserve">Circuli horarii (Stunden - Scheiben) ſunt orbes aenei, <lb/>
<anchor type="note" xlink:label="note-0136-02a" xlink:href="note-0136-02"/>
diametri 4. </s>
  <s xml:id="echoid-s2465" xml:space="preserve">digitorum, habentes peripheriam in ho-<lb/>ras, conſueta menſoribus ratione, diuiſam. </s>
  <s xml:id="echoid-s2466" xml:space="preserve">Inſtruuntur <lb/>praeterea ſinguli duabus laminis recuruis, perforatis,
<pb o="21" file="0137" n="142" rhead="GEOMETRIA SVBTERRANEA."/>
cochleisque in quolibet ſitu in circulo horario figendis, <lb/>intra quas, laxatis cochleis, circulus horarius mobilis eſt. <lb/></s>
  <s xml:id="echoid-s2467" xml:space="preserve">In centro circuli foramen fit, per quod funiculus duci <lb/>queat, et centrum ambit alius orbis mobilis unco praedi-<lb/>tus, cui alter funiculus annectitur.</s>
  <s xml:id="echoid-s2468" xml:space="preserve"/>
</p>
<div xml:id="echoid-div81" type="float" level="2" n="1">
<note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">Figur. 16.</note>
</div>
</div>
<div xml:id="echoid-div83" type="section" level="1" n="60">
<head xml:id="echoid-head77" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2469" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2470" xml:space="preserve">Tales circuli horarii adhibentur, in ferrifodinis, ubi magnes <lb/>officium non facit, pro earum directionibus reperiundis. <lb/></s>
  <s xml:id="echoid-s2471" xml:space="preserve">Debent autem duo tales circuli ad manus eſſe, pro menſione <lb/>inſtituenda.</s>
  <s xml:id="echoid-s2472" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div84" type="section" level="1" n="61">
<head xml:id="echoid-head78" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2473" xml:space="preserve">41. </s>
  <s xml:id="echoid-s2474" xml:space="preserve">His circulis horariis ſpeciatim accommodatus eſt orbis alius <lb/>
<anchor type="note" xlink:label="note-0137-01a" xlink:href="note-0137-01"/>
aeneus, medio cauus, et ſimili ratione diuiſus, uti priores <lb/>circuli; </s>
  <s xml:id="echoid-s2475" xml:space="preserve">uocatur a menſoribus transportatorium circulare, quia <lb/>illius beneficio in charta reſtituuntur anguli, circulis horariis in <lb/>ferrifodinis reperti. </s>
  <s xml:id="echoid-s2476" xml:space="preserve">ex huius transportatorii centro, exiguus an-<lb/>gulus reſectus eſt, ut in quouis caſu centrum illius orbis ad linearum <lb/>datarum extrema recte applicari poſſit.</s>
  <s xml:id="echoid-s2477" xml:space="preserve"/>
</p>
<div xml:id="echoid-div84" type="float" level="2" n="1">
<note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">Figur. 17.</note>
</div>
</div>
<div xml:id="echoid-div86" type="section" level="1" n="62">
<head xml:id="echoid-head79" xml:space="preserve">SCHOLION III.</head>
<p style="it">
  <s xml:id="echoid-s2478" xml:space="preserve">42. </s>
  <s xml:id="echoid-s2479" xml:space="preserve">Praeter hucusque commemorata organa, etiam alia menſo-<lb/>ribus metallicis uel neceſſaria uel ſaltem utilia ſunt. </s>
  <s xml:id="echoid-s2480" xml:space="preserve">Nem-<lb/>pe circuini, regulae, norma, ſcalae geometricae, diuerſae magnitu-<lb/>dinis, magnes eximius, pro excitanda in languidis acubus uirtute <lb/>directionis, funiculi aliquot ulna longi, item pugillares, et pro <lb/>commode transferenda in fodinas ſupellectile, perula. </s>
  <s xml:id="echoid-s2481" xml:space="preserve">v. </s>
  <s xml:id="echoid-s2482" xml:space="preserve">V<emph style="sc">OIGTEL.</emph> <lb/>Part. </s>
  <s xml:id="echoid-s2483" xml:space="preserve">III. </s>
  <s xml:id="echoid-s2484" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2485" xml:space="preserve">21. </s>
  <s xml:id="echoid-s2486" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2487" xml:space="preserve">ibid p. </s>
  <s xml:id="echoid-s2488" xml:space="preserve">29. </s>
  <s xml:id="echoid-s2489" xml:space="preserve">commendat etiam inſtrumentum <lb/>proportionale ex 5. </s>
  <s xml:id="echoid-s2490" xml:space="preserve">regulis figura parallelogramma compoſitum. </s>
  <s xml:id="echoid-s2491" xml:space="preserve">Ve-<lb/>rum tali carere ſatius uidetur, quia illius motus uix tam eſt aequabi-<lb/>lis et regularis, ut ichnographiis minore maioreue figura pingen-<lb/>dis, adhiberi ſine errore poſſit.</s>
  <s xml:id="echoid-s2492" xml:space="preserve"/>
</p>
<pb o="22" file="0138" n="143" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div87" type="section" level="1" n="63">
<head xml:id="echoid-head80" xml:space="preserve">SCHOLION IV.</head>
<p style="it">
  <s xml:id="echoid-s2493" xml:space="preserve">43. </s>
  <s xml:id="echoid-s2494" xml:space="preserve">Hactenus de inſtrumentis, quae ad geometriam ſubterr aneam <lb/>excolendam ſpectant, pro inſtituti modo explicaui. </s>
  <s xml:id="echoid-s2495" xml:space="preserve">Quoni-<lb/>am autem in iis praecipua ſunt, quae acu magnetica ueluti animan-<lb/>tur, pauca adhuc circa eam materiam addere placet. </s>
  <s xml:id="echoid-s2496" xml:space="preserve">Scilicet in-<lb/>ferius docebitur, quomodo etiam ſine ullo magnete dimenſio fodi-<lb/>narum, etſi laborioſius, et per aliquas ambages, praeſtetur. </s>
  <s xml:id="echoid-s2497" xml:space="preserve">Atta-<lb/>men cum in geometria ſubterranea, qualis nunc colitur, praeſtan-<lb/>tiſſima acus magneticae utilitas ſit, apparet exinde, artem, quam <lb/>tradere ingredior, hac forma non adeo antiquam eſſe. </s>
  <s xml:id="echoid-s2498" xml:space="preserve">Magnetis <lb/>enim uirtus, qua principes mundi partes, ſeptemtriones uidelicet <lb/>et auſtrum, reſpicit, ante ſeculum decimum quartum ignorata fuit. <lb/></s>
  <s xml:id="echoid-s2499" xml:space="preserve">Sunt quidem, qui ex <emph style="sc">Photii</emph> Bibliotheca locum afferunt, in <lb/>quo Euſebius quidam Baetuli lapidis beneficio una nocte iter ducen-<lb/>torum ſtadiorum confeciſſe dicitur; </s>
  <s xml:id="echoid-s2500" xml:space="preserve">uerum notum eſt, magnetem <lb/>lapidem, niſi liber ſit, in plagas laudatas non conuerti, ſed ſuo pon-<lb/>dere uictum quieſcere, et praeterea <emph style="sc">Photio</emph> magis de accelerati-<lb/>one, quam regimine nauis ſermo eſt. </s>
  <s xml:id="echoid-s2501" xml:space="preserve">Qui autem <emph style="sc">Alberti</emph> M. </s>
  <s xml:id="echoid-s2502" xml:space="preserve"><lb/>teſtimonio, ex opere de mineralibus lib. </s>
  <s xml:id="echoid-s2503" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2504" xml:space="preserve">tr. </s>
  <s xml:id="echoid-s2505" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2506" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2507" xml:space="preserve">6.</s>
  <s xml:id="echoid-s2508" xml:space="preserve">, nitun-<lb/>tur, ubi ex incerto quodam, ſiue apocrypho, ut uocant, Ariſtotelis libro, <lb/>de lapidibus, refert, magnetem gaudere ui apprehendendi ferrum, <lb/>et in ſeptentriönem ſeuertendi, illis reſpondit A<emph style="sc">THAN.</emph> <emph style="sc">Kirghervs</emph> <lb/>de arte magnetica lib. </s>
  <s xml:id="echoid-s2509" xml:space="preserve">I. </s>
  <s xml:id="echoid-s2510" xml:space="preserve">P. </s>
  <s xml:id="echoid-s2511" xml:space="preserve">I. </s>
  <s xml:id="echoid-s2512" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2513" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2514" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2515" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2516" xml:space="preserve">edit. </s>
  <s xml:id="echoid-s2517" xml:space="preserve">Colon. </s>
  <s xml:id="echoid-s2518" xml:space="preserve">docet nem-<lb/>pe, Albertum de ui noua magnetis, circa initium ſeculi XII, certi-<lb/>orem redditum, non auſum fuiſſe, eam defendere, ſine Ariſto-<lb/>telis auctoritate, atque adeo, ut eo facilius probaret, inſolitam et <lb/>hactenus ignotam magnetis proprietatem, Ariſtotelis aliquem librum <lb/>et teſtimonium, finxiſſe. </s>
  <s xml:id="echoid-s2519" xml:space="preserve">Verum mihi probabilius uidetur, locum <lb/>illum, in Alberti librum, ab alio ſequiore deſcriptore inſertum, <lb/>atque ideo ſuppoſitum fuiſſe, ut nouo inuento, quod ſeculi XIV. </s>
  <s xml:id="echoid-s2520" xml:space="preserve"><lb/>principio curioſorum naturae indagatorum ſcriptionibus maxime <lb/>celebrabatur, antiquitas maior conciliaretur. </s>
  <s xml:id="echoid-s2521" xml:space="preserve">Adducunt me in hanc <lb/>ſententiam <emph style="sc">Georgii</emph> <emph style="sc">Agricolae</emph> uerba, quae lib. </s>
  <s xml:id="echoid-s2522" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2523" xml:space="preserve">de na-<lb/>tura foſſilium p. </s>
  <s xml:id="echoid-s2524" xml:space="preserve">246. </s>
  <s xml:id="echoid-s2525" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s2526" xml:space="preserve">Baſil. </s>
  <s xml:id="echoid-s2527" xml:space="preserve">1558. </s>
  <s xml:id="echoid-s2528" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2529" xml:space="preserve">leguntur; </s>
  <s xml:id="echoid-s2530" xml:space="preserve">Albertus M. </s>
  <s xml:id="echoid-s2531" xml:space="preserve"><lb/>inquit, ſua aetate magnetem inuentum eſſe ſcribit, qui una <lb/>parte ferrum ad ſe traheret, abigeret a ſe altera contraria.</s>
  <s xml:id="echoid-s2532" xml:space="preserve">
<pb o="23" file="0139" n="144" rhead="GEOMETRIA SVBTERRANEA."/>
Hanc enim uirtutem exercet magnes in ferrum, altero polo magne-<lb/>tico tactum, et potentiore ui directionis in ſeptentrionis uel auſtri <lb/>plagam, (nam alias notum eſt, ferra leuia et libera, ut acus, etiam <lb/>ſine magnetis affrictu boream reſpicere. </s>
  <s xml:id="echoid-s2533" xml:space="preserve">uid. </s>
  <s xml:id="echoid-s2534" xml:space="preserve">notata in §. </s>
  <s xml:id="echoid-s2535" xml:space="preserve">30. </s>
  <s xml:id="echoid-s2536" xml:space="preserve">inſti-<lb/>tutionum aſtronomicarum, et add. </s>
  <s xml:id="echoid-s2537" xml:space="preserve"><emph style="sc">Voigtel</emph> p. </s>
  <s xml:id="echoid-s2538" xml:space="preserve">25.) </s>
  <s xml:id="echoid-s2539" xml:space="preserve">inſtru-<lb/>ctum, ſiquidem polus contrarius eam partem ferri, quae ab altero <lb/>polo magnetiſmo infecta eſt, repellit. </s>
  <s xml:id="echoid-s2540" xml:space="preserve">Nec in magnis ferri portio-<lb/>nibus, quae ob ponderis inertiam, haud facile moueri poſſunt, id <lb/>magnes efficit, ſed in exilioribus, quales ſunt acus ferreae, quibus <lb/>magnetica uis tactu lapidis communicata eſt. </s>
  <s xml:id="echoid-s2541" xml:space="preserve">Sequitur ergo ex illa <lb/>confeſſione Alberti, quam Agricola allegauit, eum magnetis uim <lb/>ſe dirigendi tum adhuc ignoraſſe. </s>
  <s xml:id="echoid-s2542" xml:space="preserve">Ea enim 'perſpecta, ſtatim in-<lb/>telligitur, aduerſa polorum facultas, quippe cuius effectus in oculos <lb/>cadunt, quando magnes ad acum ſua ui imbutam admouetur. </s>
  <s xml:id="echoid-s2543" xml:space="preserve">Cum <lb/>praeterea opinio eorum, qui <emph style="sc">Marcvm</emph> <emph style="sc">Pavlvm</emph> <emph style="sc">Venetvm</emph>, <lb/>ex China attuliſſe uſum acus contendunt, admodum dubia et in-<lb/>certa ſit, merito, Kircherum ſecuti, exiſtimamus, primum <emph style="sc">Ioannem</emph> <lb/><emph style="sc">Goiam</emph>, amalphitanum, artis nauticae peritum, circa annum <lb/>Chriſti 1302, cum magnetis directionem uel ipſe reperiſſet, uel ab <lb/>aliis didiciſſet, docuiſſe, quomodo lamellae ferreae, affrictu lapidis <lb/>magnetici, ſimili niſu inſtruantur, et ad nauigationes feliciore <lb/>ſucceſſu proſequendas adhibeantur. </s>
  <s xml:id="echoid-s2544" xml:space="preserve">Siquidem conſtat, iſto demum <lb/>tempore nautas, pyxide duce, iter facere coepiſſe Sed diu tamen <lb/>ante floruerunt in germania fodinae, quamuis etiam earum primae <lb/>origines obſcurae ſint, et fere lateant. </s>
  <s xml:id="echoid-s2545" xml:space="preserve"><emph style="sc">Tacitvs</emph> de germa-<lb/>norum moribus cap. </s>
  <s xml:id="echoid-s2546" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2547" xml:space="preserve">ſcribit. </s>
  <s xml:id="echoid-s2548" xml:space="preserve">Argentum et aurum pro-<lb/>pitii an irati dii negauerint, dubito; </s>
  <s xml:id="echoid-s2549" xml:space="preserve">Nec tamen affirmaue-<lb/>rim, nullam germaniae uenam argentum aurumue gignere, <lb/>quis enim ſcrutatus eſt? </s>
  <s xml:id="echoid-s2550" xml:space="preserve">Poſſeſſione et uſu haud perinde afficiun-<lb/>tur. </s>
  <s xml:id="echoid-s2551" xml:space="preserve"><emph style="sc">Plinivs</emph>, etſi Tacito coaeuus, eidem aduerſatur, et hiſtoriae <lb/>naturalis libro 34. </s>
  <s xml:id="echoid-s2552" xml:space="preserve">c. </s>
  <s xml:id="echoid-s2553" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2554" xml:space="preserve">teſtis eſt, ſua aetate in germania aeris <lb/>metallum repertum fuiſſe. </s>
  <s xml:id="echoid-s2555" xml:space="preserve"><emph style="sc">Petrvs</emph> uero <emph style="sc">Albinvs</emph> in der <lb/>Meiſniſchen Berg - Chronica, tit. </s>
  <s xml:id="echoid-s2556" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2557" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2558" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2559" xml:space="preserve">ex Ottone Friſin-<lb/>genſi, et Sigeberto Gemblacenſi, docet, ſub Ottone magno ſeculo <lb/>X. </s>
  <s xml:id="echoid-s2560" xml:space="preserve">uenas argenti ferrique Goslariae primum eſſe repertas. <lb/></s>
  <s xml:id="echoid-s2561" xml:space="preserve">Freibergenſes argenti fodinas anno 1157. </s>
  <s xml:id="echoid-s2562" xml:space="preserve">initium habuiſſe, <emph style="sc">Agri-</emph> <lb/><emph style="sc">COLA</emph> in dialogo, cui titulum Bermanni fecit, p. </s>
  <s xml:id="echoid-s2563" xml:space="preserve">419, affirmat. </s>
  <s xml:id="echoid-s2564" xml:space="preserve"><lb/><emph style="sc">Albinvs</emph> annum 1169 praefert. </s>
  <s xml:id="echoid-s2565" xml:space="preserve">Cum itaque cultura fodinarum eo
<pb o="24" file="0140" n="145" rhead="GEOMETRIA SVBTERRANEA."/>
tempore coeperit, quo diſeiplinae liberales, inprimis mathematicae, <lb/>in Europa fere ubiuis neſciebantur, conſequenseſt, artem fodi-<lb/>nas accuratius metiendi, non niſi ſero admodum ad illos labores, <lb/>periculoſiſſimos promouendos ſecurioreſque reddendos, acceſſiſſe.</s>
  <s xml:id="echoid-s2566" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div88" type="section" level="1" n="64">
<head xml:id="echoid-head81" xml:space="preserve">SCHOLION V.</head>
<p style="it">
  <s xml:id="echoid-s2567" xml:space="preserve">44. </s>
  <s xml:id="echoid-s2568" xml:space="preserve">Sed ex diuerticulo in uiam redeamus. </s>
  <s xml:id="echoid-s2569" xml:space="preserve">Traditis uocabulorum <lb/>technicorum, et organorum deſcriptionibus, tempus uideba-<lb/>tur, etiam fundamenta iacere ſcientiae, geometr arum methodo com-<lb/>ponendae. </s>
  <s xml:id="echoid-s2570" xml:space="preserve">Verum cum eadem et perpauca, et ex geometria et tri-<lb/>gonometria iam perſpicue cognita, et ſuis locis in matheſeos uniuerſae <lb/>inſtitutionibus, ex quibus nonnunquam paragraphi uncis concluſi, <lb/>breuitatis ſtudio commemorantur, ſatis explicata ſint, puto eorum <lb/>repetitione me hic ſuperſedere poſſe, ſatis habens, ſi fontes illorum <lb/>principiorum quouis loco in ipſa tractatione indicentur. </s>
  <s xml:id="echoid-s2571" xml:space="preserve">Interea <lb/>generatim moneo, pleraque, quae in ſequentibus dicentur, ad trian-<lb/>gulum rectangulum, et eius latera, nec non ad dimenſionem angu-<lb/>lorum, inuentionem ſinuum eorundem, repraeſentationem linea-<lb/>rum, beneficio ſcalarum geometricarum, et ſimilia uulgaria tum <lb/>theoremata, tum problemata, pertinere.</s>
  <s xml:id="echoid-s2572" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div89" type="section" level="1" n="65">
<head xml:id="echoid-head82" xml:space="preserve">THEOREMA.</head>
<p style="it">
  <s xml:id="echoid-s2573" xml:space="preserve">45. </s>
  <s xml:id="echoid-s2574" xml:space="preserve">Filum in libella pondere attractum, monſtrat <lb/>
<anchor type="note" xlink:label="note-0140-01a" xlink:href="note-0140-01"/>
gradus anguli acuti C, qui eſt in triangulo <lb/>rectangulo ad baſin.</s>
  <s xml:id="echoid-s2575" xml:space="preserve"/>
</p>
<div xml:id="echoid-div89" type="float" level="2" n="1">
<note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">Figur. 8.</note>
</div>
<p>
  <s xml:id="echoid-s2576" xml:space="preserve">Demonſtratio. </s>
  <s xml:id="echoid-s2577" xml:space="preserve">Nam filum a i ſemper indicat <lb/>trianguli perpendiculum, (§. </s>
  <s xml:id="echoid-s2578" xml:space="preserve">34. </s>
  <s xml:id="echoid-s2579" xml:space="preserve">35. </s>
  <s xml:id="echoid-s2580" xml:space="preserve">Geometr.) <lb/></s>
  <s xml:id="echoid-s2581" xml:space="preserve">et arcus i n metitur angulum acutum, qui eſt in tri-<lb/>anguli rectanguli uertice, ergo arcus complementi, <lb/>ſiue reſiduus in quadrante e i, angulum comple-<lb/>menti ad baſin C metitur, (§. </s>
  <s xml:id="echoid-s2582" xml:space="preserve">64. </s>
  <s xml:id="echoid-s2583" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s2584" xml:space="preserve">ſiquidem
<pb o="25" file="0141" n="146" rhead="GEOMETRIA SVBTERRANEA."/>
apparet ex intuitu ſchematis tertii, gradus in libel-<lb/>la a ſemicirculi medio numerari, ergo filum pon-<lb/>dere in libella tractum indicat numerum graduum <lb/>anguli, qui in triangulo rectangulo eſt ad baſin, <lb/>Q.</s>
  <s xml:id="echoid-s2585" xml:space="preserve">E.</s>
  <s xml:id="echoid-s2586" xml:space="preserve">D.</s>
  <s xml:id="echoid-s2587" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div91" type="section" level="1" n="66">
<head xml:id="echoid-head83" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2588" xml:space="preserve">46. </s>
  <s xml:id="echoid-s2589" xml:space="preserve">Quando autem libella e funiculo ſuſpenditur, euidens <lb/>eſt, funiculi longitudinem, manifeſtare trianguli re-<lb/>ctanguli abc hypotenuſam, ſiue ſurſum ſiue deorſum funicu-<lb/>lus ducatur. </s>
  <s xml:id="echoid-s2590" xml:space="preserve">atque adeo, in triangulo rectangulo quouis, an-<lb/>gulos et hypotenuſam innoteſcere, ex quibus crura inueſti-<lb/>gare oportet.</s>
  <s xml:id="echoid-s2591" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div92" type="section" level="1" n="67">
<head xml:id="echoid-head84" xml:space="preserve">PROBLEMA I.</head>
<p style="it">
  <s xml:id="echoid-s2592" xml:space="preserve">47. </s>
  <s xml:id="echoid-s2593" xml:space="preserve">Data hypotenuſa et angulis trianguli rectanguli, inuenire <lb/>cathetum et baſin.</s>
  <s xml:id="echoid-s2594" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2595" xml:space="preserve">Reſolutio prima iam data eſt in §. </s>
  <s xml:id="echoid-s2596" xml:space="preserve">35. </s>
  <s xml:id="echoid-s2597" xml:space="preserve">Trigon. </s>
  <s xml:id="echoid-s2598" xml:space="preserve">plan. <lb/></s>
  <s xml:id="echoid-s2599" xml:space="preserve">
<anchor type="note" xlink:label="note-0141-01a" xlink:href="note-0141-01"/>
nempe aſſumitur hypotenuſa AC pro ſinu toto, et crura <lb/>CB, BA, ſunt ſinus recti oppoſitorum angulorum. </s>
  <s xml:id="echoid-s2600" xml:space="preserve">Qua-<lb/>re infertur, pro perpendiculo, <lb/>Sin. </s>
  <s xml:id="echoid-s2601" xml:space="preserve">B: </s>
  <s xml:id="echoid-s2602" xml:space="preserve">CA = Sin C: </s>
  <s xml:id="echoid-s2603" xml:space="preserve">AB. <lb/></s>
  <s xml:id="echoid-s2604" xml:space="preserve">et pro baſi <lb/>Sin. </s>
  <s xml:id="echoid-s2605" xml:space="preserve">B: </s>
  <s xml:id="echoid-s2606" xml:space="preserve">CA = Sin. </s>
  <s xml:id="echoid-s2607" xml:space="preserve">A: </s>
  <s xml:id="echoid-s2608" xml:space="preserve">CB</s>
</p>
<div xml:id="echoid-div92" type="float" level="2" n="1">
<note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">Figur. 2.</note>
</div>
</div>
<div xml:id="echoid-div94" type="section" level="1" n="68">
<head xml:id="echoid-head85" xml:space="preserve">EXEMPLVM</head>
<p>
  <s xml:id="echoid-s2609" xml:space="preserve">Sit ac hypotenuſa 6 uln. </s>
  <s xml:id="echoid-s2610" xml:space="preserve">angulus c 10 gr. </s>
  <s xml:id="echoid-s2611" xml:space="preserve">fiat, pro cathe-<lb/>
<anchor type="note" xlink:label="note-0141-02a" xlink:href="note-0141-02"/>
to ab, ut ſinus ang. </s>
  <s xml:id="echoid-s2612" xml:space="preserve">b 90 gr. </s>
  <s xml:id="echoid-s2613" xml:space="preserve">100000 ad ac 6 uln. </s>
  <s xml:id="echoid-s2614" xml:space="preserve">ita ſinus <lb/>10 gr. </s>
  <s xml:id="echoid-s2615" xml:space="preserve">{17364--6/104184} <lb/>{104184/100000} | 1 Uln. </s>
  <s xml:id="echoid-s2616" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s2617" xml:space="preserve">Lacht. </s>
  <s xml:id="echoid-s2618" xml:space="preserve">{418/10000} fiant partes octauae, (acht-
<pb o="26" file="0142" n="147" rhead="GEOMETRIA SVBTERRANEA."/>
theile) multiplicando numeratorem per 8, et factum diuiden-<lb/>do per denominatorem. </s>
  <s xml:id="echoid-s2619" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2620" xml:space="preserve">83. </s>
  <s xml:id="echoid-s2621" xml:space="preserve">arithm. </s>
  <s xml:id="echoid-s2622" xml:space="preserve">num. </s>
  <s xml:id="echoid-s2623" xml:space="preserve">2.) <lb/></s>
  <s xml:id="echoid-s2624" xml:space="preserve">{418--8/3344/10000} ‘ 0 octauae et {33/100} <lb/>h.</s>
  <s xml:id="echoid-s2625" xml:space="preserve">e. </s>
  <s xml:id="echoid-s2626" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2627" xml:space="preserve">digiti 3 minuta ſiue ſcrupuli (§. </s>
  <s xml:id="echoid-s2628" xml:space="preserve">16) = catheto ab. </s>
  <s xml:id="echoid-s2629" xml:space="preserve"><lb/>pro baſi bc <lb/>ſinus ang. </s>
  <s xml:id="echoid-s2630" xml:space="preserve">b. </s>
  <s xml:id="echoid-s2631" xml:space="preserve">100000 ad ac 6 uln. </s>
  <s xml:id="echoid-s2632" xml:space="preserve">ita ſin. </s>
  <s xml:id="echoid-s2633" xml:space="preserve">a 80 gr. </s>
  <s xml:id="echoid-s2634" xml:space="preserve">{98480--6/590880} <lb/>{590880/100000} | 5 Uln. </s>
  <s xml:id="echoid-s2635" xml:space="preserve">{908/1000} ſiue 7 oct. </s>
  <s xml:id="echoid-s2636" xml:space="preserve">2 dig. </s>
  <s xml:id="echoid-s2637" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2638" xml:space="preserve">ſcrupul. </s>
  <s xml:id="echoid-s2639" xml:space="preserve"><lb/>quod ſi uero cum <emph style="sc">Voigtelio</emph> perpetua decimalis proportio <lb/>partium ulnae metallicae ſeruetur, multo adhuc facilior eſt <lb/>reductio, quia cum numeris uulgaribus illa proportio conue-<lb/>nit. </s>
  <s xml:id="echoid-s2640" xml:space="preserve">Ideoque in primo exemplo, datis {104184/100000}, reſoluto nu-<lb/>mero, habentur 1 uln. </s>
  <s xml:id="echoid-s2641" xml:space="preserve">o minutum primum. </s>
  <s xml:id="echoid-s2642" xml:space="preserve">4 ſecunda. </s>
  <s xml:id="echoid-s2643" xml:space="preserve">1 terti-<lb/>um. </s>
  <s xml:id="echoid-s2644" xml:space="preserve">et in caſu ſecundo 5908 ſunt 5 uln. </s>
  <s xml:id="echoid-s2645" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2646" xml:space="preserve">pr. </s>
  <s xml:id="echoid-s2647" xml:space="preserve">o ſec. </s>
  <s xml:id="echoid-s2648" xml:space="preserve">8 tert.</s>
  <s xml:id="echoid-s2649" xml:space="preserve"/>
</p>
<div xml:id="echoid-div94" type="float" level="2" n="1">
<note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">Figur. 8.</note>
</div>
<p>
  <s xml:id="echoid-s2650" xml:space="preserve">Reſotutio ſecunda. </s>
  <s xml:id="echoid-s2651" xml:space="preserve">Sola etiam ſcala geometrica accurate di-<lb/>uiſa, una cum transportatorio, ſoluendo illi problemati ſuffi-<lb/>cit. </s>
  <s xml:id="echoid-s2652" xml:space="preserve">nempe inuentus angulus c inſtrumento goniometrico de-<lb/>finitur, et ei hypotenuſa, ac itidem nota applicatur, ita defi-<lb/>deratum, tum perpendiculum, tum baſis, component figu-<lb/>ram trianguli rectanguli, et ex eadem ſcala, qua hypotenuſa <lb/>menſurata eſt, aſſumi poſſunt. </s>
  <s xml:id="echoid-s2653" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2654" xml:space="preserve">50. </s>
  <s xml:id="echoid-s2655" xml:space="preserve">Geom.)</s>
  <s xml:id="echoid-s2656" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2657" xml:space="preserve">Reſolutio tertia fit tabularum adminiculo, ſed de ea ſe-<lb/>quenti problemate copioſius dicetur.</s>
  <s xml:id="echoid-s2658" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div96" type="section" level="1" n="69">
<head xml:id="echoid-head86" xml:space="preserve">PROBLEMA II.</head>
<p style="it">
  <s xml:id="echoid-s2659" xml:space="preserve">48. </s>
  <s xml:id="echoid-s2660" xml:space="preserve">Tabulas componere, ex quibus abſque laborioſo calculo cathe-<lb/>tus et baſis trianguli rectanguli, quae datae hypotenuſae, et <lb/>angulo eidem adiacenti, reſpondent, excerpi queant.</s>
  <s xml:id="echoid-s2661" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2662" xml:space="preserve">Reſolutio 1. </s>
  <s xml:id="echoid-s2663" xml:space="preserve">Quod ad tabularum compoſitionem atti-<lb/>net, ea prima praecedentis problematis ſolutione perfici-
<pb o="27" file="0143" n="148" rhead="GEOMETRIA SVBTERRANEA."/>
tur, et tantum illud notatur, tabulas accommodatas eſſe li-<lb/>bellis, quae gradus in partes 4 diuiſos habent, fiquidem tot <lb/>partes ad geometriae ſubterraneae ſcopum obtinendum <lb/>ſufficiunt.</s>
  <s xml:id="echoid-s2664" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2665" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2666" xml:space="preserve">Exhibentur autem angulorum a libella indicato-<lb/>rum gradus in prima ſiniſtra et ultima columna dextra, et <lb/>ita quidem, ut utrinque in illis columnis complementa ad <lb/>quadrantem ponantur, ſiquidem in triangulo rectangulo, <lb/>crura ſunt ſinus oppoſitorum angulorum acutorum, hypo-<lb/>tenufa pro ſinu toto aſſumta. </s>
  <s xml:id="echoid-s2667" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2668" xml:space="preserve">27. </s>
  <s xml:id="echoid-s2669" xml:space="preserve">Trigon. </s>
  <s xml:id="echoid-s2670" xml:space="preserve">Pl.) </s>
  <s xml:id="echoid-s2671" xml:space="preserve">iſtos autem <lb/>angulos iunctos rectam componere, ex geometriae primis <lb/>elementis notum eſt. </s>
  <s xml:id="echoid-s2672" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2673" xml:space="preserve">63. </s>
  <s xml:id="echoid-s2674" xml:space="preserve">64. </s>
  <s xml:id="echoid-s2675" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s2676" xml:space="preserve">in columna uero <lb/>ſiniſtra deorſum gradus numerantur, quando ex hypotenu-<lb/>ſa et angulo cathetus quaeritur; </s>
  <s xml:id="echoid-s2677" xml:space="preserve">quando autem, ex hypo-<lb/>tenuſa et angulo, baſis deſideratur, anguli in dextra colu-<lb/>mna quaeruntur, et gradus ſurſum numerantur, prouti et-<lb/>iam poſita in principio et fine, catheti et baſeos nomi-<lb/>na indicant.</s>
  <s xml:id="echoid-s2678" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2679" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2680" xml:space="preserve">In fronte tabularum poſiti numeri, deſignant hy-<lb/>potenuſas, ſiue funiculorum longitudines. </s>
  <s xml:id="echoid-s2681" xml:space="preserve">praemittuntur <lb/>partes octauae et quartae alicuius ulnae, poſtea ulnae in-<lb/>tegrae ſequuntur. </s>
  <s xml:id="echoid-s2682" xml:space="preserve">in quarum quidem numero intermediae <lb/>quaedam deſunt, ſed eaedem reliquarum compoſitione <lb/>producuntur. </s>
  <s xml:id="echoid-s2683" xml:space="preserve">Nimirum ex praecedente monito, quo-<lb/>modo hypotenuſae in fronte, anguli uero pro catheto et <lb/>baſi in ſiniſtra et dextra columna reperiantur, dictum eſt, <lb/>utroque caſu in communi area, quae ſuperiori et a latere po-<lb/>ſito numero reſpondet, magnitudo perpendiculi uel ba-<lb/>ſeos optata occurrit. </s>
  <s xml:id="echoid-s2684" xml:space="preserve">et quando unus tantum obuius in illa <lb/>area eſt numerus, uti ſub principium contingit, ſerupuli, <lb/>ſiue decimae digiti partes, eodem ſignificantur. </s>
  <s xml:id="echoid-s2685" xml:space="preserve">Ubi duae <lb/>notae uel numeri conſpiciuntur, prima ſiniſterior digitos,
<pb o="28" file="0144" n="149" rhead="GEOMETRIA SVBTERRANEA."/>
altera decimales digiti minutias, quas ſcrupulos uocaui-<lb/>mus, denotat. </s>
  <s xml:id="echoid-s2686" xml:space="preserve">Quando tres numeri in area habentur, <lb/>primus ſiniſter octauas partes ulnae, ſequens et medius di-<lb/>gitos, tertius ſcrupulos digiti refert. </s>
  <s xml:id="echoid-s2687" xml:space="preserve">Quarta denique et <lb/>quinta nota ſiniſtra, integras ulnas indicat.</s>
  <s xml:id="echoid-s2688" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2689" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2690" xml:space="preserve">Quando uero hypotenuſa data non accurate <lb/>in numeris frontis reperitur, tum, pro proxime minore <lb/>numero et angulo, quaeritur cathetus uel baſis, et pro re-<lb/>ſidua parte uel appendice, ſeruato eodem angulo, inueſti-<lb/>gatur particula catheto uel baſi addenda. </s>
  <s xml:id="echoid-s2691" xml:space="preserve">cum enim idem <lb/>angulus ad baſin C retinetur, oriuntur duo triangula fh C, <lb/>
<anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/>
et ABC ſimilia, utpote aequiangula, in quibus latera <lb/>aequalibus angulis oppoſita ſunt proportionalia, (§. </s>
  <s xml:id="echoid-s2692" xml:space="preserve">68. <lb/></s>
  <s xml:id="echoid-s2693" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s2694" xml:space="preserve">unde analogia, ualet Cf: </s>
  <s xml:id="echoid-s2695" xml:space="preserve">fH = AC: </s>
  <s xml:id="echoid-s2696" xml:space="preserve">AB, uel <lb/>Cf † AC: </s>
  <s xml:id="echoid-s2697" xml:space="preserve">fH † AB = Cf: </s>
  <s xml:id="echoid-s2698" xml:space="preserve">fh = AC: </s>
  <s xml:id="echoid-s2699" xml:space="preserve">AB. </s>
  <s xml:id="echoid-s2700" xml:space="preserve"><lb/>(§. </s>
  <s xml:id="echoid-s2701" xml:space="preserve">40. </s>
  <s xml:id="echoid-s2702" xml:space="preserve">Analyſ. </s>
  <s xml:id="echoid-s2703" xml:space="preserve">ſinitor et §. </s>
  <s xml:id="echoid-s2704" xml:space="preserve">56. </s>
  <s xml:id="echoid-s2705" xml:space="preserve">Arithm.) </s>
  <s xml:id="echoid-s2706" xml:space="preserve">nam a: </s>
  <s xml:id="echoid-s2707" xml:space="preserve">ea = b: </s>
  <s xml:id="echoid-s2708" xml:space="preserve"><lb/>eb et a † b: </s>
  <s xml:id="echoid-s2709" xml:space="preserve">ea † eb = a: </s>
  <s xml:id="echoid-s2710" xml:space="preserve">ea = b: </s>
  <s xml:id="echoid-s2711" xml:space="preserve">eb.</s>
  <s xml:id="echoid-s2712" xml:space="preserve"/>
</p>
<div xml:id="echoid-div96" type="float" level="2" n="1">
<note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">Figur. 12.</note>
</div>
<p>
  <s xml:id="echoid-s2713" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2714" xml:space="preserve">Si etiam hypotenuſa praeter ulnas, et octauas <lb/>eius partes, digitos aliquos complectitur, ope regulae au-<lb/>reae iisdem perpendiculi uel baſeos particulae aptantur, <lb/>dum pars octaua angulo dato reſpondens in digitos decem <lb/>reſoluta ponitur.</s>
  <s xml:id="echoid-s2715" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div98" type="section" level="1" n="70">
<head xml:id="echoid-head87" xml:space="preserve">EXEMPLVM I.</head>
<p>
  <s xml:id="echoid-s2716" xml:space="preserve">Quaeritur perpendiculum pro angulo 12 {1/2} gr. </s>
  <s xml:id="echoid-s2717" xml:space="preserve">et hypote-<lb/>nuſa 6 Uln. </s>
  <s xml:id="echoid-s2718" xml:space="preserve">prior numerus in ſiniſtra columna, alter in fronte <lb/>deprehenditur, et in communi area eſt cathetus 1238 h. </s>
  <s xml:id="echoid-s2719" xml:space="preserve">e. <lb/></s>
  <s xml:id="echoid-s2720" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2721" xml:space="preserve">Uln. </s>
  <s xml:id="echoid-s2722" xml:space="preserve">2 octau. </s>
  <s xml:id="echoid-s2723" xml:space="preserve">3 {8/10} dig.</s>
  <s xml:id="echoid-s2724" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2725" xml:space="preserve">iterum qu. </s>
  <s xml:id="echoid-s2726" xml:space="preserve">baſis pro angulo 17. </s>
  <s xml:id="echoid-s2727" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s2728" xml:space="preserve">et hypotenuſa 5 Uln. <lb/></s>
  <s xml:id="echoid-s2729" xml:space="preserve">prior numerus in columna dextra, alter in fronte occurrit,
<pb o="29" file="0145" n="150" rhead="GEOMETRIA SVBTERRANEA."/>
communis area habet baſin 4625, h. </s>
  <s xml:id="echoid-s2730" xml:space="preserve">e. </s>
  <s xml:id="echoid-s2731" xml:space="preserve">4 Uln. </s>
  <s xml:id="echoid-s2732" xml:space="preserve">6 octau. <lb/></s>
  <s xml:id="echoid-s2733" xml:space="preserve">2 {5/10} dig.</s>
  <s xml:id="echoid-s2734" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div99" type="section" level="1" n="71">
<head xml:id="echoid-head88" xml:space="preserve">EXEMPLVM II.</head>
<p>
  <s xml:id="echoid-s2735" xml:space="preserve">Porro pro angulo 4 {1/4} gr. </s>
  <s xml:id="echoid-s2736" xml:space="preserve">et hypotenuſa 5 Uln. </s>
  <s xml:id="echoid-s2737" xml:space="preserve">quaeritur <lb/>perpendiculum. </s>
  <s xml:id="echoid-s2738" xml:space="preserve">Primum angulus 4 gr. </s>
  <s xml:id="echoid-s2739" xml:space="preserve">in columna tabulae <lb/>ſiniſtra occurrit, &amp; </s>
  <s xml:id="echoid-s2740" xml:space="preserve">ſub hypotenuſa 5 Uln. </s>
  <s xml:id="echoid-s2741" xml:space="preserve">reſpondent eidem <lb/>279 partes. </s>
  <s xml:id="echoid-s2742" xml:space="preserve">ſed pro {1/4} gr. </s>
  <s xml:id="echoid-s2743" xml:space="preserve">et eadem hypotenuſa 5 uln. </s>
  <s xml:id="echoid-s2744" xml:space="preserve">dantur <lb/>17. </s>
  <s xml:id="echoid-s2745" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2746" xml:space="preserve">ſumma eſt 296, ſiue 2 oct. </s>
  <s xml:id="echoid-s2747" xml:space="preserve">9 {6/10} dig. </s>
  <s xml:id="echoid-s2748" xml:space="preserve">pro catheto dati <lb/>anguli.</s>
  <s xml:id="echoid-s2749" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div100" type="section" level="1" n="72">
<head xml:id="echoid-head89" xml:space="preserve">EXEMPLVM III.</head>
<p>
  <s xml:id="echoid-s2750" xml:space="preserve">Si hypotenuſae adhaererent digiti. </s>
  <s xml:id="echoid-s2751" xml:space="preserve">ut 6 Uln. </s>
  <s xml:id="echoid-s2752" xml:space="preserve">7 digiti. </s>
  <s xml:id="echoid-s2753" xml:space="preserve">pro <lb/>angulo 16 gr. </s>
  <s xml:id="echoid-s2754" xml:space="preserve">quaeritur perpendiculum. </s>
  <s xml:id="echoid-s2755" xml:space="preserve">pro 6 ulnis eadem eſt <lb/>1523. </s>
  <s xml:id="echoid-s2756" xml:space="preserve">pro parte octaua ſiue 10 digitis (§. </s>
  <s xml:id="echoid-s2757" xml:space="preserve">16) 27. </s>
  <s xml:id="echoid-s2758" xml:space="preserve">inferatur: <lb/></s>
  <s xml:id="echoid-s2759" xml:space="preserve">10. </s>
  <s xml:id="echoid-s2760" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s2761" xml:space="preserve">dant 27 quot 7 dig. </s>
  <s xml:id="echoid-s2762" xml:space="preserve">f. </s>
  <s xml:id="echoid-s2763" xml:space="preserve">18 {9/10} h. </s>
  <s xml:id="echoid-s2764" xml:space="preserve">e. </s>
  <s xml:id="echoid-s2765" xml:space="preserve">unus digitus cum {8/10} <lb/>digiti partibus.</s>
  <s xml:id="echoid-s2766" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div101" type="section" level="1" n="73">
<head xml:id="echoid-head90" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2767" xml:space="preserve">49. </s>
  <s xml:id="echoid-s2768" xml:space="preserve">Ceterum, ſi cui placet ex ueteribus tabulis, in quibus <lb/>ulnae metallicae 800 minuta tribuuntur, nouas Voig-<lb/>telianas, decimali proportioni accommodatas componere, fa-<lb/>cilis erit reductio, et comparatio, aurea trium regula abſoluenda. <lb/></s>
  <s xml:id="echoid-s2769" xml:space="preserve">Nam perſpicuum eſt, in integris diſcrimen nullum eſle, ſed idem <lb/>ſaltem in adhàerentibus partibus octauis, digitis et minutiis <lb/>occurrere. </s>
  <s xml:id="echoid-s2770" xml:space="preserve">itaque dat@ aliquo tabularum noſtrarum numero, <lb/>v. </s>
  <s xml:id="echoid-s2771" xml:space="preserve">g. </s>
  <s xml:id="echoid-s2772" xml:space="preserve">pro hypotenuſa 6 Uln. </s>
  <s xml:id="echoid-s2773" xml:space="preserve">et angulo 40 datur perpendicu-<lb/>lum 3685, omittantur ulnae integrae, et appendix 685, quae
<pb o="30" file="0146" n="151" rhead="GEOMETRIA SVBTERRANEA."/>
ſummae 800 minutorum competit, contendatur cum ſumma <lb/>1000 minutorum, hac analogia:</s>
  <s xml:id="echoid-s2774" xml:space="preserve"/>
</p>
<note position="right" xml:space="preserve">800: # 685 # = # 1000: # 856 uel <lb/>8: # 685 # = # 10: # 856 <lb/>4: # 685 # = # 5: # 856</note>
<p>
  <s xml:id="echoid-s2775" xml:space="preserve">Itaque illi hypotenuſae et angulo in tabulis Voigtelii re-<lb/>ſpondebunt 3 Uln. </s>
  <s xml:id="echoid-s2776" xml:space="preserve">8 m. </s>
  <s xml:id="echoid-s2777" xml:space="preserve">5 ſ. </s>
  <s xml:id="echoid-s2778" xml:space="preserve">6 tert. </s>
  <s xml:id="echoid-s2779" xml:space="preserve"><emph style="sc">Voigtel</emph>, p. </s>
  <s xml:id="echoid-s2780" xml:space="preserve">53 habet <lb/>3857, quia reſiduam in diuiſione fractionem negligere noluit. <lb/></s>
  <s xml:id="echoid-s2781" xml:space="preserve">Et cum huius analogiae ſolutio, ob ciphras primo et tertio nu-<lb/>mero annexas, et quia magni numeri 800, 1000, ad paruos <lb/>aeque rationales 4: </s>
  <s xml:id="echoid-s2782" xml:space="preserve">5 reduci poſſunt, facilis ſit, apparet, ex <lb/>tabulis ſequentibus Voigtelianas integras non adeo taedioſa <lb/>opera componi, et propterea recte hoc loco ueteres et uſita-<lb/>tas menſoribus noſtris tabulas, nouis et nondum receptis an-<lb/>teferri. </s>
  <s xml:id="echoid-s2783" xml:space="preserve">Interim <emph style="sc">Voigtelivs</emph>, qui ueteres tabulas omiſit, <lb/>indicem tamen numerorum commutatorum a 1000 uſque ad <lb/>1 continuatum dedit. </s>
  <s xml:id="echoid-s2784" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2785" xml:space="preserve">62. </s>
  <s xml:id="echoid-s2786" xml:space="preserve">ſq.</s>
  <s xml:id="echoid-s2787" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div102" type="section" level="1" n="74">
<head xml:id="echoid-head91" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2788" xml:space="preserve">50. </s>
  <s xml:id="echoid-s2789" xml:space="preserve">Vt autem inuentio perpendiculorum et baſium trianguli re-<lb/>ctanguli, qua perpetuo menſores fodinarum opus babent, <lb/>facilitetur, operae pretium uiſum eſt, tabulas eum in finem compo-<lb/>ſitas bic inſerere.</s>
  <s xml:id="echoid-s2790" xml:space="preserve"/>
</p>
<pb o="31" file="0147" n="152"/>
</div>
<div xml:id="echoid-div103" type="section" level="1" n="75">
<head xml:id="echoid-head92" xml:space="preserve">TABVLAE <lb/>PERPENDICVLORVM <lb/>ET <lb/>BASIVM <lb/>TRIANGVLI RECTANGVLI.</head>
<pb file="0148" n="153"/>
<pb file="0149" n="154"/>
<note position="right" xml:space="preserve"><emph style="bf">Tabulae perpendiculorum &amp; baſium.</emph> <lb/># {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/>{1/4} # --00 # --00 # --01 # --02 # --03 # --06 # --10 # --13 # --17 # --20 # --34 # --69 <lb/>{1/2} # --00 # --01 # --03 # --05 # --06 # --13 # --20 # --27 # --34 # --41 # --69 # -139 <lb/>{3/4} # --01 # --02 # --05 # --07 # --10 # --20 # --31 # --41 # --52 # --62 # -104 # -209 <lb/>1 # --01 # --03 # --06 # --10 # --13 # --27 # --41 # --55 # --69 # --83 # -139 # -279 # 89 <lb/># --02 # --04 # --08 # --13 # --17 # --34 # --52 # --69 # --87 # -104 # -174 # -349 <lb/># --02 # --05 # --10 # --15 # --20 # --41 # --62 # --83 # -104 # -125 # -209 # -418 <lb/># --03 # --06 # --12 # --18 # --24 # --48 # --73 # --97 # -122 # -146 # -244 # -488 <lb/>2 # --03 # --06 # --13 # --20 # --27 # --55 # --83 # -111 # -139 # -167 # -279 # -558 # 88 <lb/># --03 # --07 # --15 # --23 # --31 # --62 # --94 # -125 # -157 # -188 # -314 # -628 <lb/># --04 # --08 # --17 # --26 # --34 # --69 # -104 # -139 # -174 # -209 # -348 # -697 <lb/># --04 # --09 # --19 # --28 # --38 # --76 # -115 # -153 # -191 # -230 # -383 # -767 <lb/>3 # --05 # --10 # --20 # --31 # --41 # --83 # -125 # -167 # -209 # -251 # -418 # 1-37 # 87 <lb/># --05 # --11 # --22 # --34 # --45 # --90 # -136 # -181 # -226 # -272 # -453 # 1107 <lb/># --06 # --12 # --24 # --36 # --48 # --97 # -146 # -195 # -244 # -292 # -488 # 1176 <lb/># --06 # --13 # --26 # --39 # --52 # -104 # -156 # -209 # -261 # -313 # -523 # 1246 <lb/>4 # --06 # --13 # --27 # --41 # --55 # -111 # -167 # -223 # -279 # -334 # -558 # 1316 # 86 <lb/># --07 # --14 # --29 # --44 # --59 # -118 # -177 # -237 # -296 # -355 # -592 # 1385 <lb/># --07 # --15 # --31 # --47 # --62 # -125 # -188 # -251 # -313 # -376 # -627 # 1455 <lb/># --08 # --16 # --33 # --49 # --66 # -132 # -198 # -264 # -331 # -397 # -662 # 1524 <lb/>5 # --08 # --17 # --34 # --52 # --69 # -139 # -209 # -278 # -348 # -418 # -697 # 1594 # 85</note>
<pb file="0150" n="155"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --09 # --18 # --36 # --54 # --73 # -146 # -219 # -292 # -366 # -439 # -732 # 1664 <lb/># --09 # --19 # --38 # --57 # --76 # -153 # -230 # -306 # -383 # -460 # -766 # 1733 <lb/># --10 # --20 # --40 # --60 # --80 # -160 # -240 # -320 # -400 # -480 # 1001 # 2-03 <lb/>6 # --10 # --20 # --41 # --62 # --83 # -167 # -250 # -334 # -418 # -491 # 1036 # 2-72 # 84 <lb/># --10 # --21 # --43 # --65 # --87 # -174 # -261 # -348 # -435 # -522 # 1-70 # 2141 <lb/># --11 # --22 # --45 # --67 # --90 # -181 # -271 # -362 # -452 # -543 # 1105 # 2211 <lb/># --11 # --23 # --47 # --70 # --94 # -188 # -282 # -376 # -470 # -564 # 1140 # 2280 <lb/>7 # --12 # --24 # --48 # --73 # --97 # -195 # -292 # -389 # -487 # -584 # 1174 # 2349 # 83 <lb/># --12 # --25 # --50 # --75 # -100 # -201 # -302 # -403 # -504 # -605 # 1209 # 2419 <lb/># --13 # --26 # --52 # --78 # -104 # -208 # -313 # -417 # -522 # -626 # 1244 # 2488 <lb/># --13 # --26 # --53 # --80 # -107 # -215 # -323 # -431 # -539 # -647 # 1278 # 2557 <lb/>8 # --13 # --27 # --55 # --83 # -111 # -222 # -333 # -445 # -556 # -667 # 1313 # 2626 # 82 <lb/># --14 # --28 # --57 # --86 # -114 # -229 # -344 # -459 # -573 # -688 # 1347 # 2695 <lb/># --14 # --29 # --59 # --88 # -118 # -236 # -354 # -472 # -591 # -709 # 1382 # 2764 <lb/># --15 # --30 # --60 # --91 # -121 # -243 # -365 # -486 # -608 # -780 # 1416 # 3-33 <lb/>9 # --15 # --32 # --62 # --93 # -125 # -250 # -375 # -500 # -625 # -750 # 1451 # 3102 # 81 <lb/># --16 # --32 # --64 # --96 # -128 # -257 # -385 # -514 # -642 # -771 # 1485 # 3171 <lb/># --16 # --33 # --66 # --99 # -132 # -264 # -396 # -528 # -660 # -792 # 1520 # 3240 <lb/># --16 # --33 # --67 # -101 # -135 # -270 # -406 # -541 # -677 # 1-12 # 1554 # 3309 <lb/>10 # --17 # --34 # --69 # -104 # -138 # -277 # -416 # -555 # -694 # 1-33 # 1589 # 3378 # 80</note>
<pb file="0151" n="156"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --17 # --35 # --71 # -106 # -142 # -284 # -427 # -569 # -711 # 1-54 # 1623 # 3447 <lb/># --18 # --36 # --72 # -109 # -145 # -291 # -437 # -583 # -728 # 1-74 # 1657 # 3515 <lb/># --18 # --37 # --74 # -111 # -149 # -298 # -447 # -596 # -746 # 1-95 # 1692 # 3584 <lb/>11 # --19 # --38 # --76 # -114 # -152 # -305 # -457 # -610 # -763 # 1115 # 1726 # 3652 # 79 <lb/># --19 # --39 # --78 # -117 # -156 # -312 # -468 # -624 # -780 # 1136 # 1760 # 3721 <lb/># --19 # --39 # --79 # -119 # -159 # -318 # -478 # -637 # -797 # 1158 # 1794 # 3789 <lb/># --20 # --40 # --81 # -122 # -162 # -325 # -488 # -651 # 1-14 # 1178 # 2-29 # 4-58 <lb/>12 # --20 # --41 # --83 # -124 # -166 # -332 # -498 # -665 # 1-31 # 1197 # 2-63 # 4126 # 78 <lb/># --21 # --42 # --84 # -127 # -169 # -339 # -509 # -678 # 1-48 # 1218 # 2-97 # 4194 <lb/># --21 # --43 # --86 # -129 # -173 # -346 # -519 # -692 # 1-65 # 1238 # 2131 # 4263 <lb/># --22 # --44 # --88 # -132 # -176 # -353 # -529 # -706 # 1-82 # 1259 # 2165 # 4331 <lb/>13 # --22 # --44 # --89 # -134 # -179 # -359 # -539 # -719 # 1-99 # 1279 # 2199 # 4399 # 77 <lb/># --22 # --45 # --91 # -137 # -183 # -366 # -550 # -733 # 1166 # 1300 # 2233 # 4467 <lb/># --23 # --46 # --93 # -140 # -186 # -373 # -560 # -744 # 1133 # 1320 # 2267 # 4535 <lb/># --23 # --47 # --95 # -142 # -190 # -380 # -570 # -760 # 1150 # 1341 # 2301 # 4602 <lb/>14 # --24 # --48 # --96 # -145 # -193 # -387 # -580 # -774 # 1167 # 1361 # 2335 # 4670 # 76 <lb/># --24 # --49 # --98 # -147 # -196 # -393 # -590 # -787 # 1184 # 1381 # 2369 # 4738 <lb/># --25 # --50 # -100 # -150 # -200 # -400 # -600 # 1001 # 1201 # 1401 # 2401 # 5006 <lb/># --25 # --50 # -101 # -152 # -203 # -407 # -611 # 1-14 # 1218 # 1422 # 2436 # 5-73 <lb/>15 # --25 # --51 # -103 # -155 # -207 # -414 # -621 # 1-28 # 1235 # 1442 # 2470 # 5141 # 75</note>
<pb file="0152" n="157"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --26 # --52 # -105 # -157 # -210 # -420 # -631 # 1-41 # 1252 # 1462 # 2504 # 5208 <lb/># --26 # --53 # -106 # -160 # -213 # -427 # -641 # 1-55 # 1268 # 1482 # 2537 # 5275 <lb/># --27 # --54 # -108 # -162 # -217 # -434 # -651 # 1-68 # 1285 # 1502 # 2571 # 5343 <lb/>16 # --27 # --55 # -110 # -165 # -220 # -441 # -661 # 1-82 # 1302 # 1523 # 2605 # 5410 # 74 <lb/># --27 # --55 # -111 # -167 # -223 # -447 # -671 # 1-95 # 1319 # 1543 # 2638 # 5477 <lb/># --28 # --56 # -113 # -170 # -227 # -454 # -681 # 1108 # 1336 # 1563 # 2672 # 5544 <lb/># --28 # --57 # -115 # -172 # -230 # -461 # -691 # 1122 # 1352 # 1583 # 2705 # 5611 <lb/>17 # --29 # --58 # -116 # -175 # -233 # -467 # -701 # 1135 # 1369 # 1603 # 2738 # 5677 # 73 <lb/># --29 # --59 # -118 # -177 # -237 # -474 # -711 # 1148 # 1386 # 1623 # 2772 # 5744 <lb/># --30 # --60 # -120 # -180 # -240 # -481 # -721 # 1162 # 1402 # 1643 # 3005 # 6-11 <lb/># --30 # --60 # -121 # -182 # -243 # -487 # -731 # 1175 # 1419 # 1663 # 3-38 # 6-77 <lb/>18 # --30 # --61 # -123 # -185 # -247 # -494 # -741 # 1188 # 1436 # 1683 # 3-72 # 6144 # 72 <lb/># --31 # --62 # -125 # -187 # -250 # -501 # -751 # 1202 # 1452 # 1703 # 3105 # 6210 <lb/># --31 # --63 # -126 # -190 # -253 # -507 # -761 # 1215 # 1469 # 1723 # 3138 # 6276 <lb/># --32 # --64 # -128 # -192 # -257 # -514 # -771 # 1228 # 1485 # 1742 # 3171 # 6343 <lb/>19 # --32 # --65 # -130 # -195 # -260 # -520 # -781 # 1241 # 1502 # 1762 # 3204 # 6409 # 71 <lb/># --32 # --65 # -131 # -197 # -263 # -527 # -791 # 1255 # 1518 # 1782 # 3237 # 6475 <lb/># --33 # --66 # -133 # -200 # -267 # -534 # 1001 # 1268 # 1535 # 1792 # 3270 # 6540 <lb/># --33 # --67 # -135 # -202 # -270 # -540 # 1-10 # 1281 # 1551 # 2-21 # 3303 # 6606 <lb/>20 # --34 # --68 # -136 # -205 # -273 # -547 # 1-20 # 1294 # 1568 # 2-41 # 3336 # 6672 # 70</note>
<pb file="0153" n="158"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --34 # --69 # -138 # -206 # -276 # -553 # 1-30 # 1207 # 1584 # 2-61 # 3368 # 6737 <lb/># --35 # --70 # -140 # -210 # -280 # -560 # 1-40 # 1320 # 1600 # 2-80 # 3401 # 7-03 <lb/># --35 # --70 # -141 # -212 # -283 # -566 # 1-50 # 1333 # 1617 # 2100 # 3434 # 7-68 <lb/>21 # --36 # --71 # -143 # -215 # -286 # -573 # 1-60 # 1346 # 1633 # 2120 # 3466 # 7133 # 69 <lb/># --36 # --72 # -144 # -217 # -289 # -579 # 1-69 # 1359 # 1649 # 2139 # 3499 # 7199 <lb/># --36 # --73 # -146 # -219 # -293 # -586 # 1-79 # 1372 # 1666 # 2159 # 3552 # 4264 <lb/># --37 # --74 # -148 # -222 # -296 # -892 # 1-89 # 1385 # 1682 # 2178 # 3564 # 7328 <lb/>22 # --37 # --74 # -149 # -224 # -299 # -499 # 1-99 # 1398 # 1698 # 2198 # 3596 # 7393 # 68 <lb/># --37 # --75 # -151 # -227 # -302 # -605 # 1108 # 1411 # 1714 # 2217 # 3629 # 7458 <lb/># --38 # --76 # -153 # -229 # -306 # -612 # 1118 # 1424 # 1730 # 2236 # 3661 # 7522 <lb/># --38 # --77 # -154 # -232 # -309 # -618 # 1128 # 1437 # 1746 # 2256 # 3693 # 7587 <lb/>23 # --39 # --78 # -156 # -234 # -312 # -625 # 1137 # 1450 # 1762 # 2275 # 3725 # 7651 # 67 <lb/># --39 # --78 # -157 # -236 # -315 # -631 # 1147 # 1463 # 1778 # 2294 # 3757 # 7715 <lb/># --39 # --79 # -159 # -239 # -318 # -637 # 1156 # 1475 # 1794 # 2313 # 3789 # 7779 <lb/># --40 # --80 # -161 # -241 # -322 # -644 # 1166 # 1488 # 2010 # 2333 # 4-21 # 8-43 <lb/>24 # --40 # --81 # -162 # -244 # -325 # -650 # 1176 # 1501 # 2026 # 2352 # 4-53 # 8107 # 66 <lb/># --41 # --82 # -164 # -246 # -328 # -657 # 1185 # 1514 # 2-42 # 2371 # 4-85 # 8171 <lb/># --41 # --82 # -165 # -248 # -331 # -663 # 1195 # 1527 # 2-58 # 2390 # 4117 # 8235 <lb/># --41 # --83 # -167 # -251 # -334 # -669 # 1204 # 1539 # 2-74 # 2409 # 4149 # 8298 <lb/>25 # --42 # --84 # -169 # -253 # -338 # -676 # 1214 # 1552 # 2-90 # 2428 # 4180 # 8361 # 65</note>
<pb file="0154" n="159"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --42 # --85 # -170 # -255 # -341 # -682 # 1223 # 1565 # 2106 # 2447 # 4212 # 8425 <lb/># --43 # --86 # -172 # -258 # -344 # -688 # 1233 # 1577 # 2122 # 2466 # 4244 # 8488 <lb/># --43 # --86 # -173 # -262 # -347 # -695 # 1242 # 1590 # 2137 # 2485 # 4275 # 8551 <lb/>26 # --43 # --87 # -175 # -264 # -350 # -701 # 1252 # 1602 # 2153 # 2504 # 4306 # 8613 # 64 <lb/># --44 # --88 # -176 # -265 # -353 # -707 # 1261 # 1616 # 2169 # 2522 # 4338 # 8670 <lb/># --44 # --89 # -178 # -267 # -356 # -713 # 1270 # 1627 # 2184 # 2541 # 4369 # 8739 <lb/># --45 # --90 # -180 # -270 # -360 # -720 # 1280 # 1640 # 2200 # 2560 # 4400 # 9-01 <lb/>27 # --45 # --90 # -180 # -272 # -363 # -726 # 1289 # 1652 # 2215 # 2579 # 4431 # 9-63 # 63 <lb/># --45 # --91 # -183 # -274 # -366 # -732 # 1299 # 1665 # 2231 # 2598 # 4463 # 9127 <lb/># --46 # --92 # -184 # -276 # -369 # -738 # 1308 # 1677 # 2246 # 2616 # 4493 # 9187 <lb/># --46 # --93 # -186 # -279 # -372 # -744 # 1317 # 1689 # 2262 # 2634 # 4524 # 9249 <lb/>28 # --46 # --93 # -187 # -280 # -375 # -751 # 1326 # 1702 # 2277 # 2653 # 4555 # 9311 # 62 <lb/># --47 # --94 # -189 # -283 # -378 # -757 # 1335 # 1714 # 2293 # 2671 # 4586 # 9372 <lb/># --47 # --95 # -190 # -286 # -381 # -763 # 1345 # 1726 # 2308 # 2690 # 4616 # 9433 <lb/># --48 # --96 # -192 # -288 # -384 # -769 # 1354 # 1738 # 2323 # 2708 # 4647 # 9494 <lb/>29 # --48 # --96 # -193 # -289 # -387 # -775 # 13@3 # 1751 # 2339 # 2727 # 4678 # 9556 # 61 <lb/># --48 # --97 # -195 # -293 # -390 # -781 # 1372 # 1763 # 2354 # 2745 # 4708 # 9617 <lb/># --49 # --98 # -196 # -295 # -393 # -787 # 1381 # 1775 # 2369 # 2763 # 4739 # 9678 <lb/># --49 # --99 # -198 # -297 # -396 # -793 # 1390 # 1787 # 2384 # 2781 # 4769 # 9739 <lb/>30 # --50 # -1-- # -2-- # -3-- # -4-- # 1--- # 14-- # 2--- # 24-- # 3--- # 5--- # 10--- # 60</note>
<pb file="0155" n="160"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --50 # -1-- # -201 # -301 # -403 # 1-06 # 1409 # 2-12 # 2415 # 3-18 # 5-30 # 10060 <lb/># --50 # -101 # -203 # -304 # -406 # 1-12 # 1418 # 2-24 # 2430 # 3-36 # 5-60 # 10120 <lb/># --51 # -102 # -204 # -306 # -409 # 1-18 # 1427 # 2-36 # 2445 # 3-54 # 5-90 # 10180 <lb/>31 # --51 # -103 # -206 # -309 # -412 # 1-24 # 1436 # 2-48 # 2460 # 3-72 # 5120 # 10240 # 59 <lb/># --51 # -103 # -207 # -311 # -414 # 1-29 # 1444 # 2-59 # 2474 # 3-89 # 5149 # 10299 <lb/># --52 # -104 # -208 # -313 # -417 # 1-35 # 1453 # 2-71 # 2489 # 3107 # 5179 # 10358 <lb/># --52 # -105 # -210 # -315 # -420 # 1-41 # 1462 # 2-83 # 2504 # 3125 # 5209 # 10419 <lb/>32 # --52 # -106 # -211 # -316 # -423 # 1-47 # 1471 # 2-95 # 2519 # 3143 # 5239 # 10478 # 58 <lb/># --53 # -106 # -213 # -319 # -426 # 1-53 # 1480 # 2107 # 2534 # 3161 # 5268 # 10537 <lb/># --53 # -107 # -214 # -322 # -429 # 1-59 # 1489 # 2119 # 2548 # 3178 # 5297 # 10595 <lb/># --54 # -108 # -216 # -324 # -432 # 1-65 # 1498 # 2130 # 2563 # 3196 # 5327 # 10654 <lb/>33 # --54 # -108 # -217 # -325 # -435 # 1-71 # 1507 # 2142 # 2578 # 3214 # 5357 # 10714 # 57 <lb/># --54 # -109 # -219 # -328 # -438 # 1-77 # 1515 # 2154 # 2592 # 3231 # 5385 # 10771 <lb/># --55 # -110 # -220 # -331 # -441 # 1-83 # 1524 # 2166 # 2607 # 3249 # 5415 # 11-30 <lb/># --55 # -111 # -222 # -333 # -444 # 1-88 # 1533 # 2177 # 2622 # 3266 # 5444 # 11-88 <lb/>34 # --55 # -111 # -223 # -334 # -447 # 1@94 # 1542 # 2189 # 2636 # 3284 # 5473 # 11147 # 56 <lb/># --56 # -112 # -225 # -337 # -450 # 1100 # 1550 # 2200 # 2652 # 3301 # 5502 # 11204 <lb/># --56 # -113 # -226 # -339 # -453 # 1106 # 1559 # 2212 # 2665 # 3310 # 5531 # 11262 <lb/># --56 # -113 # -227 # -341 # -455 # 1111 # 1567 # 2223 # 2679 # 3335 # 5559 # 11318 <lb/>35 # --57 # -114 # -229 # -343 # -458 # 1117 # 1576 # 2235 # 2694 # 3353 # 5588 # 11377 # 55</note>
<pb file="0156" n="161"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --57 # -115 # -230 # -346 # -461 # 1123 # 1585 # 2246 # 2708 # 3370 # 5616 # 11433 <lb/># --58 # -116 # -232 # -348 # -464 # 1129 # 1593 # 2258 # 2722 # 3387 # 5645 # 11491 <lb/># --58 # -116 # -233 # -350 # -467 # 1134 # 1602 # 2269 # 2736 # 3404 # 5673 # 11547 <lb/>36 # --58 # -117 # -235 # -352 # -470 # 1140 # 1610 # 2280 # 2751 # 3421 # 5702 # 11604 # 54 <lb/># --59 # -118 # -236 # -354 # -473 # 1146 # 1619 # 2292 # 2765 # 3438 # 5730 # 11660 <lb/># --59 # -118 # -237 # -356 # -475 # 1151 # 1627 # 2303 # 2779 # 3455 # 5758 # 11716 <lb/># --59 # -119 # -239 # -358 # -478 # 1157 # 1635 # 2314 # 2793 # 3471 # 5786 # 11772 <lb/>37 # --60 # -120 # -240 # -360 # -481 # 1162 # 1644 # 2325 # 3007 # 3484 # 6-14 # 12-28 # 53 <lb/># --60 # -121 # -242 # -363 # -484 # 1168 # 1652 # 2336 # 3-20 # 3504 # 6-41 # 12-83 <lb/># --60 # -121 # -243 # -365 # -487 # 1174 # 1661 # 2348 # 3-35 # 3522 # 6-70 # 12140 <lb/># --61 # -122 # -244 # -367 # -489 # 1179 # 1669 # 2359 # 3-48 # 3538 # 6-97 # 12195 <lb/>38 # --61 # -123 # -246 # -369 # -492 # 1185 # 1677 # 2370 # 3-62 # 3555 # 6125 # 12250 # 52 <lb/># --61 # -123 # -247 # -371 # -495 # 1190 # 1685 # 2380 # 3-76 # 3571 # 6152 # 12304 <lb/># --62 # -124 # -249 # -373 # -498 # 1196 # 1694 # 2392 # 3-90 # 3588 # 6180 # 12360 <lb/># --62 # -125 # -250 # -375 # -500 # 1201 # 1702 # 2402 # 3103 # 3604 # 6207 # 12414 <lb/>39 # --62 # -125 # -251 # -376 # -503 # 1206 # 171@ # 2413 # 3117 # 3620 # 6234 # 12469 # 51 <lb/># --63 # -126 # -253 # -379 # -506 # 1212 # 1718 # 2424 # 3130 # 3636 # 6261 # 12523 <lb/># --63 # -127 # -254 # -381 # -508 # 1217 # 1726 # 2435 # 3144 # 3652 # 6288 # 12576 <lb/># --63 # -127 # -255 # -382 # -511 # 1223 # 1734 # 2446 # 3157 # 3669 # 6315 # 12631 <lb/>40 # --64 # -128 # -257 # -385 # -514 # 1228 # 1742 # 2456 # 3171 # 3685 # 6352 # 12684 # 50</note>
<pb file="0157" n="162"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --64 # -129 # -258 # -387 # -516 # 1233 # 1750 # 2467 # 3184 # 3710 # 6368 # 12737 <lb/># --64 # -129 # -259 # -389 # -519 # 1239 # 1758 # 2478 # 3197 # 3717 # 6395 # 12790 <lb/># --65 # -130 # -261 # -391 # -522 # 1244 # 1766 # 2488 # 3210 # 3732 # 6421 # 13-43 <lb/>41 # --65 # -131 # -262 # -393 # -524 # 1249 # 1774 # 2499 # 3224 # 3759 # 6448 # 13-96 # 49 <lb/># --65 # -131 # -263 # -395 # -527 # 1254 # 1782 # 2509 # 3237 # 3764 # 6474 # 13148 <lb/># --66 # -132 # -265 # -397 # -530 # 1260 # 1790 # 2520 # 3250 # 3780 # 65-- # 13201 <lb/># --66 # -133 # -266 # -399 # -532 # 1265 # 1797 # 2530 # 3263 # 3795 # 6526 # 13252 <lb/>42 # --66 # -133 # -267 # -4-- # -535 # 1270 # 2-05 # 2541 # 3276 # 4-11 # 6553 # 13306 # 48 <lb/># --67 # -134 # -268 # -403 # -537 # 1275 # 2-13 # 2551 # 3289 # 4-27 # 6678 # 13356 <lb/># --67 # -135 # -270 # -405 # -540 # 1280 # 2-21 # 2561 # 3302 # 4-42 # 6604 # 13408 <lb/># --67 # -135 # -271 # -407 # -543 # 1286 # 2-29 # 2572 # 3315 # 4-58 # 6630 # 13460 <lb/>43 # --68 # -136 # -272 # -408 # -545 # 1291 # 2-36 # 2582 # 3327 # 4-73 # 6655 # 13511 # 47 <lb/># --68 # -137 # -274 # -410 # -548 # 1296 # 2-44 # 2592 # 3340 # 4-88 # 6680 # 13561 <lb/># --68 # -137 # -275 # -412 # -550 # 1301 # 2-52 # 2602 # 3353 # 4104 # 6706 # 13613 <lb/># --69 # -138 # -276 # -414 # -553 # 1306 # 2-59 # 2612 # 3366 # 4119 # 6732 # 13664 <lb/>44 # --69 # -138 # -277 # -416 # -555 # 1311 # 2-67 # 2622 # 3378 # 4134 # 6757 # 13714 # 46 <lb/># --69 # -139 # -279 # -418 # -558 # 1316 # 2-74 # 2632 # 3390 # 4148 # 6781 # 13763 <lb/># --70 # -140 # -280 # -420 # -560 # 1321 # 2-82 # 2642 # 3403 # 4164 # 7-07 # 14-14 <lb/># --70 # -140 # -281 # -421 # -563 # 1326 # 2-89 # 2652 # 3416 # 4179 # 7-32 # 14-64 <lb/>45 # --70 # -141 # -282 # -423 # -565 # 1331 # 2-97 # 2662 # 3428 # 4194 # 7-56 # 14113 # 45</note>
<pb file="0158" n="163"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --71 # -142 # -284 # -426 # -568 # 1336 # 2104 # 2672 # 3440 # 4208 # 7-80 # 14161 <lb/># --71 # -142 # -285 # -427 # -570 # 1341 # 2111 # 2682 # 3452 # 4223 # 7105 # 14211 <lb/># --71 # -143 # -286 # -429 # -573 # 1346 # 2119 # 2692 # 3465 # 4238 # 7130 # 14260 <lb/>46 # --71 # -143 # -287 # -431 # -575 # 1350 # 2126 # 2701 # 3477 # 4252 # 7154 # 14309 # 44 <lb/># --72 # -144 # -288 # -433 # -577 # 1355 # 2133 # 2711 # 3489 # 4267 # 7178 # 14356 <lb/># --72 # -145 # -290 # -435 # -580 # 1360 # 2140 # 2721 # 3501 # 4281 # 7202 # 14405 <lb/># --72 # -145 # -291 # -436 # -582 # 1365 # 2147 # 2730 # 3513 # 4295 # 7226 # 14452 <lb/>47 # --73 # -146 # -292 # -438 # -585 # 1370 # 2155 # 2740 # 3525 # 4310 # 7250 # 14501 # 43 <lb/># --73 # -146 # -293 # -440 # -587 # 1374 # 2162 # 2749 # 3537 # 4324 # 7274 # 14548 <lb/># --73 # -147 # -294 # -442 # -589 # 1379 # 2169 # 2759 # 3548 # 4338 # 7297 # 14595 <lb/># --74 # -148 # -296 # -444 # -592 # 1384 # 2176 # 2768 # 3560 # 1352 # 7321 # 14643 <lb/>48 # --74 # -148 # -297 # -445 # -594 # 1389 # 2183 # 2778 # 3572 # 4367 # 7345 # 14690 # 42 <lb/># --74 # -149 # -298 # -447 # -596 # 1393 # 2190 # 2787 # 3584 # 4380 # 7368 # 14736 <lb/># --74 # -149 # -299 # -449 # -599 # 1398 # 2197 # 2796 # 3595 # 4394 # 7391 # 14782 <lb/># --75 # -150 # -3-- # -450 # -601 # 1402 # 2204 # 3-05 # 3607 # 4408 # 7414 # 15-28 <lb/>49 # --75 # -150 # -301 # -452 # -603 # 1407 # 2211 # 3-15 # 3618 # 4422 # 7437 # 15-75 # 41 <lb/># --75 # -151 # -303 # -454 # -605 # 1412 # 2218 # 3-24 # 3630 # 4436 # 7460 # 15120 <lb/># --76 # -152 # -304 # -456 # -6-8 # 1416 # 2224 # 3-33 # 3641 # 4449 # 7482 # 15166 <lb/># --76 # -152 # -305 # -457 # -610 # 1421 # 2231 # 3-42 # 3652 # 4463 # 7505 # 15211 <lb/>50 # --76 # -153 # -306 # -459 # -612 # 1425 # 2238 # 3-51 # 3664 # 4476 # 7528 # 15256 # 40</note>
<pb file="0159" n="164"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --76 # -153 # -307 # -461 # -615 # 1430 # 2245 # 3-60 # 3675 # 4490 # 7550 # 15300 <lb/># --77 # -154 # -308 # -462 # -617 # 1434 # 2251 # 3-69 # 3686 # 4503 # 7572 # 15345 <lb/># --77 # -154 # -309 # -464 # -619 # 1438 # 2258 # 3-77 # 3697 # 4516 # 7594 # 15388 <lb/>51 # --77 # -155 # -310 # -466 # -621 # 1443 # 2265 # 3-86 # 3708 # 4530 # 7616 # 15433 # 39 <lb/># --77 # -155 # -311 # -467 # -623 # 1447 # 2271 # 3-95 # 3719 # 4543 # 7638 # 45476 <lb/># --78 # -156 # -313 # -469 # -626 # 1452 # 2278 # 3104 # 3730 # 4556 # 7660 # 15521 <lb/># --78 # -157 # -314 # -471 # -628 # 1456 # 2284 # 3112 # 3741 # 3569 # 7682 # 15564 <lb/>52 # --78 # -157 # -315 # -472 # -630 # 1460 # 2291 # 3121 # 3752 # 4582 # 7704 # 15608 # 38 <lb/># --79 # -158 # -316 # -474 # -632 # 1464 # 2297 # 3129 # 3762 # 4594 # 7724 # 15649 <lb/># --79 # -158 # -317 # -475 # -634 # 1469 # 2303 # 3138 # 3773 # 4607 # 7746 # 15692 <lb/># --79 # -159 # -318 # -477 # -636 # 1473 # 2310 # 3147 # 3784 # 4620 # 7768 # 15736 <lb/>53 # --79 # -159 # -319 # -479 # -638 # 1477 # 2315 # 3155 # 3794 # 4633 # 7788 # 15777 # 37 <lb/># --80 # -160 # -320 # -480 # -640 # 1481 # 2322 # 3163 # 4004 # 4645 # 8009 # 16-19 <lb/># --80 # -160 # -321 # -482 # -643 # 1486 # 2329 # 3172 # 4-15 # 4658 # 8-30 # 16-60 <lb/># --80 # -161 # -322 # -483 # -645 # 1490 # 2335 # 3180 # 4-25 # 4670 # 8-51 # 16103 <lb/>54 # --80 # -161 # -323 # -485 # -647 # @494 # 2341 # 3188 # 4-36 # 4683 # 8-72 # 16144 # 36 <lb/># --81 # -162 # -324 # -486 # -649 # 1498 # 2347 # 3197 # 4-46 # 4695 # 8-92 # 16185 <lb/># --81 # -162 # -325 # -488 # -651 # 1502 # 2353 # 3205 # 4-56 # 4707 # 8112 # 16225 <lb/># --81 # -163 # -326 # -489 # -653 # 1506 # 2359 # 3213 # 4-66 # 4719 # 8132 # 16265 <lb/>55 # --81 # -163 # -327 # -491 # -655 # 1510 # 2363 # 3221 # 4-76 # 4739 # 8152 # 16305 # 35</note>
<pb file="0160" n="165"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --82 # -164 # -328 # -492 # -657 # 1515 # 2371 # 3229 # 4-86 # 4743 # 8172 # 16345 <lb/># --82 # -164 # -329 # -494 # -659 # 1518 # 2377 # 3237 # 4-96 # 4755 # 8192 # 16385 <lb/># --82 # -165 # -330 # -495 # -661 # 1522 # 2383 # 3244 # 4106 # 4767 # 8212 # 16424 <lb/>56 # --82 # -165 # -331 # -496 # -663 # 1526 # 2389 # 3252 # 4116 # 4779 # 8232 # 16464 # 34 <lb/># --83 # -166 # -332 # -498 # -665 # 1530 # 2395 # 3260 # 4125 # 4790 # 8251 # 16502 <lb/># --83 # -166 # -333 # -5-- # -667 # 1538 # 2401 # 3268 # 4135 # 5-02 # 8270 # 16540 <lb/># --83 # -167 # -334 # -501 # -668 # 1537 # 2406 # 3275 # 4144 # 5-13 # 8289 # 16579 <lb/>57 # --83 # -167 # -335 # -502 # -670 # 1541 # 2412 # 3283 # 4154 # 5-25 # 8309 # 16618 # 33 <lb/># --84 # -168 # -336 # -504 # -672 # 1545 # 2418 # 3291 # 4164 # 5-38 # 8320 # 16656 <lb/># --84 # -168 # -337 # -505 # -674 # 1549 # 2424 # 3298 # 4173 # 5-84 # 8347 # 16694 <lb/># --84 # -169 # -338 # -506 # -676 # 1553 # 2429 # 3306 # 4182 # 5-59 # 8365 # 16731 <lb/>58 # --84 # -169 # -339 # -508 # -678 # 1556 # 2435 # 3313 # 4192 # 5-70 # 8384 # 16768 # 32 <lb/># --85 # -170 # -340 # -510 # -680 # 1560 # 2440 # 3320 # 4201 # 5-81 # 8402 # 17-04 <lb/># --85 # -170 # -341 # -511 # -682 # 1564 # 2446 # 3328 # 4210 # 5-92 # 8420 # 17-41 <lb/># --85 # -170 # -341 # -512 # -683 # 1567 # 2451 # 3335 # 4219 # 5103 # 8439 # 17-78 <lb/>59 # --85 # -171 # -342 # -514 # -685 # 1571 # 2457 # 3342 # 4225 # 5114 # 8457 # 17114 # 31 <lb/># --85 # -171 # -343 # -515 # -687 # 1575 # 2462 # 3350 # 4237 # 5125 # 8475 # 17150 <lb/># --86 # -172 # -344 # -516 # -689 # 1578 # 2467 # 3357 # 4246 # 5135 # 8492 # 17185 <lb/># --86 # -172 # -345 # -518 # -691 # 1582 # 2473 # 3364 # 4255 # 5146 # 8510 # 17220 <lb/>60 # --86 # -173 # -346 # -519 # -692 # 1585 # 2478 # 3371 # 4264 # 5156 # 8528 # 17256 # 30</note>
<pb file="0161" n="166"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --86 # -173 # -347 # -520 # -694 # 1589 # 2483 # 3378 # 4772 # 5167 # 8545 # 17291 <lb/># --87 # -174 # -348 # -521 # -696 # 1592 # 2488 # 3385 # 4281 # 5177 # 8562 # 17325 <lb/># --87 # -174 # -348 # -522 # -697 # 1595 # 2493 # 3391 # 4289 # 5187 # 8579 # 17359 <lb/>61 # --87 # -174 # -349 # -523 # -699 # 1599 # 2499 # 3398 # 4298 # 5198 # 8596 # 17393 # 29 <lb/># --87 # -175 # -350 # -525 # -701 # 1602 # 2504 # 3405 # 4306 # 5208 # 8613 # 17427 <lb/># --87 # -175 # -351 # -526 # -703 # 1606 # 2509 # 3412 # 4315 # 5218 # 8632 # 17460 <lb/># --88 # -176 # -352 # -528 # -704 # 1609 # 2514 # 3418 # 4323 # 5228 # 8647 # 17494 <lb/>62 # --88 # -176 # -353 # -529 # -706 # 1612 # 2519 # 3425 # 4331 # 5238 # 8663 # 17527 # 28 <lb/># --88 # -176 # -353 # -529 # -707 # 1615 # 2523 # 3431 # 4339 # 5247 # 8679 # 17559 <lb/># --88 # -177 # -354 # -531 # -709 # 1619 # 2528 # 3438 # 4344 # 5257 # 8696 # 17592 <lb/># --88 # -177 # -355 # -532 # -711 # 1622 # 2933 # 3444 # 4356 # 5267 # 8712 # 17624 <lb/>63 # --89 # -178 # -356 # -534 # -712 # 1625 # 2538 # 3451 # 4364 # 5276 # 8728 # 17656 # 27 <lb/># --89 # -178 # -357 # -535 # -714 # 1628 # 2543 # 3457 # 4371 # 5286 # 8748 # 17687 <lb/># --89 # -178 # -357 # -535 # -715 # 1631 # 2547 # 3463 # 4379 # 4295 # 8759 # 17718 <lb/># --89 # -179 # -358 # -53@ # -717 # 1634 # 2552 # 3469 # 4387 # 5304 # 8774 # 17749 <lb/>64 # --89 # -179 # -359 # -538 # -719 # @638 # 2557 # 3478 # 4395 # 5314 # 8790 # 17780 # 26 <lb/># --90 # -180 # -360 # -540 # -720 # 1641 # 2561 # 3482 # 4402 # 5323 # 9-05 # 18-11 <lb/># --90 # -180 # -361 # -541 # -722 # 1644 # 2566 # 3488 # 4410 # 5332 # 9-20 # 18-41 <lb/># --90 # -180 # -361 # -541 # -723 # 1647 # 2570 # 3494 # 4417 # 5341 # 9-35 # 18-71 <lb/>65 # --90 # -181 # -362 # -543 # -725 # 1650 # 2575 # 3500 # 4425 # 5350 # 9-50 # 18100 # 25</note>
<pb file="0162" n="167"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --90 # -181 # -363 # -544 # -726 # 1653 # 2579 # 3506 # 4432 # 5359 # 9-65 # 18130 <lb/># --90 # -181 # -363 # -544 # -727 # 1655 # 2583 # 3511 # 4439 # 5367 # 9-79 # 18159 <lb/># --91 # -182 # -364 # -546 # -729 # 1658 # 2588 # 3517 # 4447 # 5376 # 9-94 # 18188 <lb/>66 # --91 # -182 # -365 # -547 # -730 # 1661 # 2592 # 3523 # 4454 # 5384 # 9108 # 18216 # 24 <lb/># --91 # -183 # -366 # -549 # -732 # 1664 # 2596 # 3528 # 4461 # 5393 # 9122 # 18244 <lb/># --91 # -183 # -366 # -549 # -733 # 1667 # 2600 # 3534 # 4468 # 5401 # 9136 # 18272 <lb/># --91 # -183 # -367 # -550 # -735 # 1670 # 2605 # 3540 # 4476 # 5410 # 9150 # 18300 <lb/>67 # --92 # -184 # -367 # -552 # -736 # 1672 # 2609 # 3545 # 4482 # 5418 # 9164 # 18328 # 23 <lb/># --92 # -184 # -368 # -552 # -737 # 1675 # 2613 # 3551 # 4488 # 5426 # 9177 # 18355 <lb/># --92 # -184 # -369 # -553 # -739 # 1678 # 2617 # 3556 # 4495 # 5434 # 9190 # 18387 <lb/># --92 # -185 # -370 # -555 # -740 # 1680 # 2621 # 3561 # 4502 # 5442 # 9204 # 18408 <lb/>68 # --92 # -185 # -370 # -555 # -741 # 1683 # 2625 # 3566 # 4508 # 5450 # 9217 # 18434 # 22 <lb/># --92 # -185 # -371 # -556 # -743 # 1686 # 2629 # 3572 # 4515 # 5458 # 9230 # 18460 <lb/># --93 # -186 # -372 # -558 # -744 # 1688 # 2632 # 3577 # 4521 # 5465 # 9243 # 18486 <lb/># --93 # -186 # -372 # -558 # -745 # 1691 # 2636 # 3582 # 4528 # 5473 # 9256 # 18512 <lb/>69 # --93 # -186 # -373 # -559 # -746 # 1693 # 264@ # 3587 # 4534 # 5481 # 9268 # 18537 # 21 <lb/># --93 # -187 # -374 # -561 # -748 # 1696 # 2644 # 3592 # 4540 # 5488 # 9281 # 18562 <lb/># --93 # -187 # -374 # -561 # -749 # 1698 # 2648 # 3597 # 4546 # 5496 # 9293 # 18586 <lb/># --93 # -187 # -375 # -562 # -750 # 1701 # 2651 # 3602 # 4555 # 5503 # 9305 # 18611 <lb/>70 # --93 # -187 # -375 # -562 # -751 # 1703 # 2655 # 3607 # 4558 # 5510 # 9317 # 18635 # 20</note>
<pb file="0163" n="168"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --94 # -188 # -376 # -564 # -752 # 1705 # 2658 # 3611 # 4564 # 5517 # 9329 # 18658 <lb/># --94 # -188 # -377 # -565 # -754 # 1708 # 2662 # 3616 # 4570 # 5524 # 5341 # 18682 <lb/># --94 # -188 # -377 # -565 # -755 # 1710 # 2665 # 3621 # 4576 # 5531 # 9352 # 18705 <lb/>71 # --94 # -189 # -378 # -567 # -756 # 1712 # 2669 # 3625 # 4582 # 5538 # 9364 # 18728 # 19 <lb/># --94 # -189 # -378 # -567 # -757 # 1715 # 2672 # 3630 # 4587 # 5545 # 9375 # 18750 <lb/># --94 # -189 # -379 # -568 # -758 # 1717 # 2675 # 3634 # 4593 # 5551 # 9386 # 18773 <lb/># --94 # -189 # -379 # -568 # -759 # 1719 # 2679 # 3639 # 4598 # 5558 # 9397 # 18795 <lb/>72 # --95 # -190 # -380 # -570 # -760 # 1721 # 2682 # 3643 # 8604 # 5565 # 9408 # 19-16 # 18 <lb/># --95 # -190 # -380 # -570 # -761 # 1723 # 2685 # 3647 # 4609 # 5571 # 9419 # 19-38 <lb/># --95 # -190 # -381 # -571 # -762 # 1725 # 2688 # 3655 # 4614 # 5577 # 9429 # 19-59 <lb/># --95 # -191 # -382 # -573 # -764 # 1728 # 2692 # 3656 # 4620 # 5584 # 9440 # 19-80 <lb/>73 # --95 # -191 # -382 # -573 # -765 # 1730 # 2695 # 3660 # 4625 # 5590 # 9450 # 191-- # 17 <lb/># --95 # -191 # -383 # -574 # -766 # 1732 # 2698 # 3664 # 4630 # 5596 # 9460 # 19121 <lb/># --95 # -191 # -383 # -574 # -767 # 1734 # 2701 # 3668 # 4635 # 5602 # 9470 # 19140 <lb/># --96 # -192 # -384 # -576 # -768 # 1736 # 2704 # 3672 # 4640 # 5608 # 9480 # 19160 <lb/>74 # --96 # -192 # -384 # -576 # -769 # @738 # 2707 # 3676 # 4645 # 5614 # 9490 # 19180 # 16 <lb/># --96 # -192 # -384 # -576 # -769 # 1739 # 2709 # 3679 # 4649 # 5619 # 9499 # 19199 <lb/># --96 # -192 # -385 # -577 # -770 # 1740 # 2712 # 3683 # 4654 # 5625 # 9509 # 19218 <lb/># --96 # -192 # -385 # -577 # -771 # 1743 # 2715 # 3687 # 4659 # 5630 # 9518 # 19236 <lb/>75 # --96 # -193 # -386 # -579 # -772 # 1745 # 2718 # 3690 # 4663 # 5636 # 9527 # 19254 # 15</note>
<pb file="0164" n="169"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --96 # -193 # -386 # -579 # -773 # 1747 # 2720 # 3694 # 4668 # 5641 # 9536 # 19272 <lb/># --96 # -193 # -387 # -580 # -774 # 1749 # 2723 # 3698 # 4672 # 5647 # 9546 # 19290 <lb/># --96 # -193 # -387 # -580 # -775 # 1750 # 2726 # 3701 # 4676 # 5652 # 9553 # 19307 <lb/>76 # --97 # -194 # -388 # -582 # -776 # 1752 # 2728 # 3704 # 4681 # 5657 # 9562 # 19324 # 14 <lb/># --97 # -194 # -388 # -582 # -777 # 1754 # 2731 # 3708 # 4685 # 5662 # 9570 # 19344 <lb/># --97 # -194 # -388 # -582 # -777 # 1755 # 2733 # 3711 # 4689 # 5667 # 9578 # 19357 <lb/># --97 # -194 # -389 # -583 # -778 # 1757 # 2736 # 3714 # 4693 # 5672 # 9586 # 19373 <lb/>77 # --97 # -194 # -389 # -583 # -779 # 1758 # 2738 # 3717 # 4697 # 5677 # 9594 # 19389 # 13 <lb/># --97 # -195 # -390 # -585 # -780 # 1760 # 2740 # 3721 # 4701 # 5681 # 9602 # 19401 <lb/># --97 # -195 # -390 # -585 # -781 # 1762 # 2743 # 3724 # 1705 # 5686 # 9610 # 19420 <lb/># --97 # -195 # -390 # -585 # -781 # 1763 # 2745 # 3727 # 4708 # 5690 # 9617 # 19435 <lb/>78 # --97 # -195 # -391 # -586 # -782 # 1764 # 2747 # 3730 # 4712 # 5695 # 9625 # 19450 # 12 <lb/># --97 # -195 # -391 # -586 # -783 # 1766 # 2749 # 3732 # 4716 # 5699 # 9632 # 19464 <lb/># --97 # -195 # -391 # -586 # -783 # 1767 # 2751 # 3735 # 4719 # 5703 # 9639 # 19478 <lb/># --97 # -196 # -392 # -587 # -784 # 1769 # 2753 # 3738 # 4723 # 5707 # 9646 # 19492 <lb/>79 # --97 # -196 # -392 # -588 # -785 # 1770 # 2755 # 3741 # 4726 # 5711 # 9652 # 19505 # 11 <lb/># --98 # -196 # -392 # -588 # -785 # 1771 # 2757 # 3743 # 4729 # 5715 # 9659 # 19519 <lb/># --98 # -196 # -393 # -589 # -786 # 1773 # 2759 # 3746 # 4733 # 5719 # 9666 # 19532 <lb/># --98 # -196 # -393 # -589 # -787 # 1774 # 2767 # 3748 # 4736 # 5723 # 9672 # 19544 <lb/>80 # --98 # -196 # -393 # -589 # -787 # 1775 # 2763 # 3751 # 4739 # 5727 # 9678 # 19556 # 10</note>
<pb file="0165" n="170"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --98 # -197 # -394 # -591 # -788 # 1776 # 2765 # 3753 # 4742 # 5730 # 9684 # 19568 <lb/># --98 # -197 # -394 # -591 # -789 # 1778 # 2767 # 3756 # 4745 # 5734 # 9690 # 19580 <lb/># --98 # -197 # -394 # -591 # -789 # 1778 # 2768 # 3757 # 4746 # 5736 # 9693 # 19587 <lb/>81 # --98 # -197 # -395 # -592 # -790 # 1780 # 2770 # 3760 # 4750 # 5740 # 9701 # 19603 # 9 <lb/># --98 # -197 # -395 # -592 # -790 # 1781 # 2772 # 3762 # 4753 # 5744 # 9706 # 19613 <lb/># --98 # -198 # -395 # -592 # -791 # 1782 # 2773 # 3764 # 4766 # 5747 # 9710 # 19624 <lb/># --98 # -198 # -395 # -592 # -791 # 1783 # 2775 # 3766 # 4758 # 5750 # 9717 # 19634 <lb/>82 # --98 # -198 # -396 # -594 # -792 # 1784 # 2776 # 3768 # 4761 # 5753 # 9722 # 19644 # 8 <lb/># --99 # -198 # -396 # -594 # -792 # 1785 # 2778 # 3770 # 4763 # 5756 # 9726 # 19653 <lb/># --99 # -198 # -396 # -594 # -793 # 1786 # 2779 # 3772 # 4765 # 5758 # 9731 # 19663 <lb/># --99 # -198 # -396 # -594 # -793 # 1787 # 2780 # 3774 # 4768 # 3761 # 9736 # 19672 <lb/>83 # --99 # -198 # -397 # -595 # -794 # 1788 # 2782 # 3776 # 4770 # 5764 # 9740 # 19680 # 7 <lb/># --99 # -198 # -397 # -595 # -794 # 1788 # 2783 # 3777 # 4772 # 5766 # 9745 # 19680 <lb/># --99 # -198 # -397 # -595 # -794 # 1789 # 2784 # 3779 # 4774 # 5769 # 9748 # 19697 <lb/># --99 # -198 # -397 # -595 # -795 # 1790 # 2785 # 3780 # 4776 # 5771 # 9752 # 19704 <lb/>84 # --99 # -198 # -397 # -595 # -795 # 1791 # 2786 # 3782 # 4778 # 5773 # 9756 # 19712 # 6 <lb/># --99 # -198 # -397 # -595 # -795 # 1791 # 2787 # 3783 # 4779 # 5775 # 9759 # 19719 <lb/># --99 # -199 # -398 # -596 # -796 # 1792 # 2788 # 3785 # 4781 # 5777 # 9763 # 19726 <lb/># --99 # -199 # -398 # -597 # -796 # 1793 # 2789 # 3786 # 4783 # 5779 # 9766 # 19732 <lb/>85 # --99 # -199 # -398 # -597 # -796 # 1793 # 2790 # 3787 # 4784 # 5781 # 9769 # 19739 # 5</note>
<pb file="0166" n="171"/>
<note position="right" xml:space="preserve"> # {1/8} # {1/4} # {1/2} # {3/4} # 1 # 2 # 3 # 4 # 5 # 6 # 10 # 20 <lb/># --99 # -199 # -398 # -597 # -797 # 1794 # 2791 # 3789 # 4786 # 5783 # 9772 # 19745 <lb/># --99 # -199 # -398 # -597 # -797 # 1795 # 2792 # 3790 # 4787 # 5785 # 9775 # 19750 <lb/># --99 # -199 # -398 # -597 # -797 # 1795 # 2793 # 3791 # 4789 # 5786 # 9778 # 19756 <lb/>86 # --99 # -199 # -399 # -598 # -798 # 1796 # 2794 # 3792 # 4790 # 5788 # 9780 # 19761 # 4 <lb/># --99 # -199 # -399 # -598 # -798 # 1796 # 2794 # 3793 # 4791 # 5789 # 9782 # 19765 <lb/># --99 # -199 # -399 # -598 # -798 # 1797 # 2795 # 3794 # 4792 # 5791 # 9785 # 19770 <lb/># --99 # -199 # -399 # -598 # -798 # 1797 # 2796 # 3794 # 4793 # 5792 # 9787 # 19774 <lb/>87 # --99 # -199 # -399 # -598 # -798 # 1797 # 2796 # 3795 # 4794 # 5793 # 9789 # 19778 # 3 <lb/># --99 # -199 # -399 # -598 # -799 # 1798 # 2797 # 3796 # 4795 # 5794 # 9790 # 19781 <lb/># --99 # -199 # -399 # -598 # -799 # 1798 # 2797 # 3796 # 4796 # 5795 # 9792 # 19784 <lb/># --99 # -199 # -399 # -598 # -799 # 1798 # 2798 # 3797 # 4796 # 5796 # 9793 # 19787 <lb/>88 # --99 # -199 # -399 # -599 # -799 # 1799 # 2798 # 3798 # 4797 # 5797 # 6795 # 19790 # 2 <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2798 # 3798 # 4798 # 5797 # 9796 # 19792 <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3798 # 4798 # 5798 # 9797 # 19794 <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3799 # 4799 # 5798 # 9798 # 19796 <lb/>89 # --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3799 # 4799 # 5799 # 9798 # 19797 # 1 <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3799 # 4799 # 5799 # 9799 # 19798 # {3/4} <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3799 # 4799 # 5799 # 9799 # 19799 # {1/2} <lb/># --99 # -199 # -399 # -599 # -799 # 1799 # 2799 # 3799 # 4799 # 5799 # 9799 # 19799 # {1/4} <lb/>90 # -1-- # -2-- # -4-- # -6-- # 1--- # 2--- # 3--- # 4--- # 5--- # 6--- # 10-- # 20---</note>
<pb o="51" file="0167" n="172" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div104" type="section" level="1" n="76">
<head xml:id="echoid-head93" xml:space="preserve">SCHOLION II.</head>
<p>
  <s xml:id="echoid-s2791" xml:space="preserve">51. </s>
  <s xml:id="echoid-s2792" xml:space="preserve">Hactenus de apparatu geometriae ſ<unsure/>ubterraneae, et ſubſidiis <lb/>explicaui, ſequitur ut de ipſa fodinarum dimenſione agatur. <lb/></s>
  <s xml:id="echoid-s2793" xml:space="preserve">cuius quaeſtionis duo caſus ſunt, alter, ubi compaſſo uti licet, <lb/>cum nempe ferri minera magneticae acus directionem non pertur-<lb/>bat, alter, in ipſis ferri fodinis metiendis locum habet.</s>
  <s xml:id="echoid-s2794" xml:space="preserve"/>
</p>
<head xml:id="echoid-head94" xml:space="preserve">PROBLEMA III.</head>
<p style="it">
  <s xml:id="echoid-s2795" xml:space="preserve">52. </s>
  <s xml:id="echoid-s2796" xml:space="preserve">Fodinas metiri, in quibus acus magnetica a ferri minera non <lb/>turbatur.</s>
  <s xml:id="echoid-s2797" xml:space="preserve"/>
</p>
<head xml:id="echoid-head95" xml:space="preserve">RESOLVTIO PRIMA</head>
<p>
  <s xml:id="echoid-s2798" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2799" xml:space="preserve">Menſor in fodinam deſcendat, eiusque conditio-<lb/>nes contempletur, inprimis uti ſciat, ubi et qua ratione <lb/>inſtrumenta commode diſponi, et ad dimenſionem ad-<lb/>hiberi poſſint.</s>
  <s xml:id="echoid-s2800" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2801" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2802" xml:space="preserve">Antequam menſionem aggrediatúr, praeparet ſibi <lb/>in pugillaribus claſſes numerorum inſcribendorum, quas <lb/>cum ſuis titulis laterculus ſequens, ſignificat.</s>
  <s xml:id="echoid-s2803" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2804" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2805" xml:space="preserve">Funiculo cochlea firmato, uel manu in ſummo <lb/>putei ab operae ſocio prehenſo, demittatur ſuſpenſum ex <lb/>eodem pondus, quantum nempe recta altitudo permittit, <lb/>donec aliquem putei parietem feriat, menſureturque hu-<lb/>ius fili perpendicularis longitudo, et (ſubtracta tamen fu-<lb/>niculi portione, quae ſupra uel extra puteum extenſa fuit.) <lb/></s>
  <s xml:id="echoid-s2806" xml:space="preserve">in pugillaribus ſcribatur, addito angulo, qui hic eſt 90 gr. </s>
  <s xml:id="echoid-s2807" xml:space="preserve"><lb/>cum titulo cadentis lineae. </s>
  <s xml:id="echoid-s2808" xml:space="preserve">(fallendes) nam hora in puteis <lb/>perpendicularibus n@lla obſeruatur. </s>
  <s xml:id="echoid-s2809" xml:space="preserve">Ceterum ſurgentium <lb/>et cadentium ſpecuum conditiones in noſtris indicibus <lb/>latinis literis S. </s>
  <s xml:id="echoid-s2810" xml:space="preserve">et C. </s>
  <s xml:id="echoid-s2811" xml:space="preserve">ſignificabuntur.</s>
  <s xml:id="echoid-s2812" xml:space="preserve"/>
</p>
<pb o="52" file="0168" n="173" rhead="GEOMETRIA SVBTERRANEA."/>
<note position="right" xml:space="preserve"> <lb/># 1. Loca uel plagae inundi. <lb/># 2. Fod. ſurgent. l. cadent. <lb/># 3. Gradus et partes libellae. <lb/># 4. Ulnae et octau. funiculi <lb/># 5. Digiti <lb/># 6. Horae Compa@li <lb/># 7. Octauae p. horae. <lb/># 8. Signa.</note>
<p>
  <s xml:id="echoid-s2813" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2814" xml:space="preserve">Quando uero acceſſus ad ſubterraneos ſpecus obli-<lb/>quus eſt, tunc ſecundum eius, uel parietis, ductum funi-<lb/>culus dirigatur, ita tamen, ut nullibi latus parietis ſtringat, <lb/>ſed libere iuxta eundem extendatnr, et cochleis utrimque <lb/>alligetur, hinc in medio funiculi libella ſuſpendatur, eaque, <lb/>niſi uncorum ſuorum elaterio fixa haereat, ligneis paxil-<lb/>lis firmetur, ne in decliui funiculo prouoluatur, et ob-<lb/>ſeruetur obliquus angulus, (§. </s>
  <s xml:id="echoid-s2815" xml:space="preserve">45.) </s>
  <s xml:id="echoid-s2816" xml:space="preserve">quem perpendiculum <lb/>libellae in ſemicirculo definit, hunc angulum, una cum <lb/>funis longitudine, et conditione ſpecus ſurgentis uel ca-<lb/>dentis, (§. </s>
  <s xml:id="echoid-s2817" xml:space="preserve">8.) </s>
  <s xml:id="echoid-s2818" xml:space="preserve">in pugillares, ſpeciatim in claſles 2. </s>
  <s xml:id="echoid-s2819" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2820" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2821" xml:space="preserve">5. <lb/></s>
  <s xml:id="echoid-s2822" xml:space="preserve">refer. </s>
  <s xml:id="echoid-s2823" xml:space="preserve">alii in puteis obliquis libellam e funiculi duobus ex-<lb/>tremis atque adeo bis ſuſpendunt, ut eo accuratius angu-<lb/>lum reperiant, uerum, ſi bene tenſus eſt funiculus, et nul-<lb/>libi, uti decet, parietem cauernae ſtringit, ſemel ſuſpenſa <lb/>libra angulum deſideratum rite manifeſtat.</s>
  <s xml:id="echoid-s2824" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2825" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2826" xml:space="preserve">Tollatur a funiculo libra, et ex eodem ſuſpenda-<lb/>tur compaſſus, ſemper prorſum (h. </s>
  <s xml:id="echoid-s2827" xml:space="preserve">e. </s>
  <s xml:id="echoid-s2828" xml:space="preserve">in eam regionem, <lb/>in quam es progreſſurus) conuerſo puncto ſeptentrionis. <lb/></s>
  <s xml:id="echoid-s2829" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2830" xml:space="preserve">28.) </s>
  <s xml:id="echoid-s2831" xml:space="preserve">nimirum collocata intra ſuſpenſum annulum ſitu ho-<lb/>rizontali pyxide, obſerua horam et horae partem octa-
<pb o="53" file="0169" n="174" rhead="GEOMETRIA SVBTERRANEA."/>
uam, quam cuſpis acus magneticae, poſtquam requieuit, <lb/>indicat, hosque numeros prioribus in indice, claſſe 6. </s>
  <s xml:id="echoid-s2832" xml:space="preserve">7. <lb/></s>
  <s xml:id="echoid-s2833" xml:space="preserve">adſcribe, in claſſe autem prima quadrantis, cui horae <lb/>competunt, ſignum, se. </s>
  <s xml:id="echoid-s2834" xml:space="preserve">or. </s>
  <s xml:id="echoid-s2835" xml:space="preserve">me. </s>
  <s xml:id="echoid-s2836" xml:space="preserve">occ. </s>
  <s xml:id="echoid-s2837" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2838" xml:space="preserve">5.) </s>
  <s xml:id="echoid-s2839" xml:space="preserve">nota.</s>
  <s xml:id="echoid-s2840" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2841" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2842" xml:space="preserve">Vt autem eo certior reddaris de exacta horae de-<lb/>finitione, compaſſum quoque alia in parte tenſi funiculi <lb/>appende, et horam reſpice, haec ſi cum priore conſenſe-<lb/>rit, recte ſe habet declinatio obſeruata; </s>
  <s xml:id="echoid-s2843" xml:space="preserve">ſi minus reſpondeat <lb/>priori, aut in compaſſo eſt uitium, aut ferri ſubeſt minera, <lb/>quae magnetis impedit uirtutem. </s>
  <s xml:id="echoid-s2844" xml:space="preserve">Affert praeterea <lb/>Voigtelivs p. </s>
  <s xml:id="echoid-s2845" xml:space="preserve">103. </s>
  <s xml:id="echoid-s2846" xml:space="preserve">hanc cautionem, ut conuerſe in funi-<lb/>culo ſuſpendatur compaſſus, prorſum directo puncto meridiei, ſiqui-<lb/>dem, ubi alia hora ac in priore poſitione, et ita una ui-<lb/>tium compaſſi, ſignificatur, inter horas indicatas media <lb/>pro uera putatur.</s>
  <s xml:id="echoid-s2847" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2848" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2849" xml:space="preserve">Eo loco, ubi uel perpendiculum incidit, uel, quo <lb/>alterum funiculi extremum, cochlea fixum fuit, iterum <lb/>funis, per ſequentem fodinam, quamdiu eius rectitudo <lb/>permittit, continuetur, (quando tamen cauerna longior <lb/>eſt, conſultum iudicatur, funem non ultra ſex ulnas uel <lb/>orgyias metallicas extendere, ne ſuo uel inſtrumentorum <lb/>pondere curuetur, aut fallat obſeruationem lineae inclina-<lb/>tionis.) </s>
  <s xml:id="echoid-s2850" xml:space="preserve">fortiterque adductus, parallelo cum pariete alteru-<lb/>tro fodinae ſitu, cochlea figatur, iterumque, libellae et <lb/>compaſſi adminiculo, poſitus ad horizontem, et conuer-<lb/>ſio in mundi partes inueſtigentur, et cum longitudine ſu-<lb/>nis in indices referantur.</s>
  <s xml:id="echoid-s2851" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2852" xml:space="preserve">8. </s>
  <s xml:id="echoid-s2853" xml:space="preserve">Quando occurrunt in cauernis loca quaedam no-<lb/>tabilia, u. </s>
  <s xml:id="echoid-s2854" xml:space="preserve">g. </s>
  <s xml:id="echoid-s2855" xml:space="preserve">aeſtuaria, putei noui ſurſum deorſumue por-<lb/>recti, cuniculi, uenaeque laterales, ſigna lapidibus inſculpta, <lb/>extrema ſpecuum, eadem quoque competentibus locis in <lb/>pugillaribus notentur.</s>
  <s xml:id="echoid-s2856" xml:space="preserve"/>
</p>
<pb o="54" file="0170" n="175" rhead="GEOMETRIA SVBTERRANEA."/>
<p>
  <s xml:id="echoid-s2857" xml:space="preserve">9. </s>
  <s xml:id="echoid-s2858" xml:space="preserve">Imo ſpecus diuergentes, et ad latus uel deorſum <lb/>producti, ſimili artificio ſecundum ſitum duplicem menſu-<lb/>rentur, et numeri diligenter in tabulis ſcribantur.</s>
  <s xml:id="echoid-s2859" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div105" type="section" level="1" n="77">
<head xml:id="echoid-head96" xml:space="preserve">RESOLVTIO SECVNDA</head>
<p>
  <s xml:id="echoid-s2860" xml:space="preserve">Eadem ſpecuum dimenſio fieri quoque poteſt com-<lb/>paſſo iacente. </s>
  <s xml:id="echoid-s2861" xml:space="preserve">nempe</s>
</p>
<p>
  <s xml:id="echoid-s2862" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2863" xml:space="preserve">Iterum demittitur per puteum, perpendiculum, et <lb/>longitudo funis notatur. </s>
  <s xml:id="echoid-s2864" xml:space="preserve">ubi incidit perpendiculum, ibi <lb/>compaſſus, horizontali ſitu, collocatur, ita ut acus quieta <lb/>accurate immineat lineae meridianae. </s>
  <s xml:id="echoid-s2865" xml:space="preserve">fit autem haec poſi-<lb/>tio, uel cuneis ligneis ſubiectis, uel compaſſo fulcro cui-<lb/>dam impoſito, ut beneficio globi in matrice mobilis, ſitus <lb/>horizonti parallelus ei conciliari queat.</s>
  <s xml:id="echoid-s2866" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2867" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2868" xml:space="preserve">Deinde operae ſocius trahet funiculum, quousque <lb/>cauernae longitudo permittit, et menſor extremum alte-<lb/>rum funis, cui chorda tenuior alligata eſt, extendet ſuper <lb/>centrum compaſſi, ducetque regulam mobilem, ut eius <lb/>
<anchor type="note" xlink:label="note-0170-01a" xlink:href="note-0170-01"/>
linea fiduciae ſubſit funiculo, ita enim regula horam illius <lb/>ſpecus manifeſtabit.</s>
  <s xml:id="echoid-s2869" xml:space="preserve"/>
</p>
<div xml:id="echoid-div105" type="float" level="2" n="1">
<note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">Figur. 14.</note>
</div>
<p>
  <s xml:id="echoid-s2870" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2871" xml:space="preserve">Similiter in progreſſu ſe geret menſor, atque ita <lb/>compaſſo iacente linearum directiones reperiet. </s>
  <s xml:id="echoid-s2872" xml:space="preserve">Pro in-<lb/>clinationibus uero earundem reperiundis, libellam adhi-<lb/>bebit, uti in priore ſolutione eſt explicatum.</s>
  <s xml:id="echoid-s2873" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2874" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2875" xml:space="preserve">Si inuentio direction@@ fodinae, ope talis compaſſi, <lb/>qui exiguam acum habere ſolet, taedioſior aut non ſatis <lb/>certa uideatur, adhibeat pyxidem alteram, in cuius centro <lb/>
<anchor type="note" xlink:label="note-0170-02a" xlink:href="note-0170-02"/>
regula, cum unco poteſt poni, qualis figura 15 deſcribitur. <lb/></s>
  <s xml:id="echoid-s2876" xml:space="preserve">ſic enim regula funis, cum quo connexa eſt, directionem <lb/>commodius patefaciet.</s>
  <s xml:id="echoid-s2877" xml:space="preserve"/>
</p>
<div xml:id="echoid-div106" type="float" level="2" n="2">
<note position="left" xlink:label="note-0170-02" xlink:href="note-0170-02a" xml:space="preserve">Figur. 15.</note>
</div>
<pb o="55" file="0171" n="176" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div108" type="section" level="1" n="78">
<head xml:id="echoid-head97" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2878" xml:space="preserve">53. </s>
  <s xml:id="echoid-s2879" xml:space="preserve">Ex ultimae ſolutionis conſideratione cuiuis perſpicuum <lb/>eſt, eam ob ſpecuum anguſtiam, et quia in obſeruanda <lb/>hora facilius, quam in compaſſo penſili, error committitur, <lb/>priori merito poſtponi, u. </s>
  <s xml:id="echoid-s2880" xml:space="preserve">Voigtel. </s>
  <s xml:id="echoid-s2881" xml:space="preserve">p. </s>
  <s xml:id="echoid-s2882" xml:space="preserve">113.</s>
  <s xml:id="echoid-s2883" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div109" type="section" level="1" n="79">
<head xml:id="echoid-head98" xml:space="preserve">PROBLEMA IV.</head>
<p>
  <s xml:id="echoid-s2884" xml:space="preserve">54. </s>
  <s xml:id="echoid-s2885" xml:space="preserve">Ferrifodinas metiri.</s>
  <s xml:id="echoid-s2886" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2887" xml:space="preserve">Reſolutio prima. </s>
  <s xml:id="echoid-s2888" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2889" xml:space="preserve">Alliga in principio fodinae fu-<lb/>
<anchor type="note" xlink:label="note-0171-01a" xlink:href="note-0171-01"/>
niculum, et eum ſecundum axem uel parietem eius exten-<lb/>de, et in b cochlea fige.</s>
  <s xml:id="echoid-s2890" xml:space="preserve"/>
</p>
<div xml:id="echoid-div109" type="float" level="2" n="1">
<note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">Figur. 9.</note>
</div>
<p>
  <s xml:id="echoid-s2891" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2892" xml:space="preserve">Metire funem, et ſuſpenſa ex eodem libella, angu-<lb/>lum quaere.</s>
  <s xml:id="echoid-s2893" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2894" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2895" xml:space="preserve">Et quia in aditu ferrifodinarum non adeo magna <lb/>magnetis perturbatio timenda eſt, ſuſpende ex primo fu-<lb/>ne compaſſum, duobus locis, nota horam directionis, et <lb/>ſi acus non easdem circuli horarii partes indicat, utroque <lb/>extremo, elige horam, quae in ſummo, quod in ſuperfi-<lb/>ciem terrae protenditur, monſtrabatur, nam ibi minus co-<lb/>hiberi uim magneticam ueriſimile aſt, horam autem in in-<lb/>dice diligenter annota.</s>
  <s xml:id="echoid-s2896" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2897" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2898" xml:space="preserve">Tende alium funiculum be per ſequentem meatum, <lb/>atque eum cochlea firma, et libellam applica.</s>
  <s xml:id="echoid-s2899" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2900" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2901" xml:space="preserve">Vt habeatur angulus ab utroque funiculo in b fa-<lb/>ctus, alium funem c d ita duobus prioribus applica, ut re-<lb/>ctus ſit, nec a pariete aliquo cauernae curuetur. </s>
  <s xml:id="echoid-s2902" xml:space="preserve">Metire <lb/>deinceps lineas cb, bd, cd, et numeros in pugillares refer. <lb/></s>
  <s xml:id="echoid-s2903" xml:space="preserve">ſuſpende etiam ex funiculo c d libellam, ſi placet, et quan-<lb/>do ſine curuatione funium a b, b e fieri poteſt.</s>
  <s xml:id="echoid-s2904" xml:space="preserve"/>
</p>
<pb o="56" file="0172" n="177" rhead="GEOMETRIA SVBTERRANEA."/>
<p>
  <s xml:id="echoid-s2905" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2906" xml:space="preserve">Ita continua reliquorum meatuum dimenſionem, <lb/>et poteris etiam ferri fodinarum flexus indicare et in char-<lb/>ta exhibere. </s>
  <s xml:id="echoid-s2907" xml:space="preserve">quo autem id artificio agatur, poſtea doce-<lb/>bitur.</s>
  <s xml:id="echoid-s2908" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2909" xml:space="preserve">Reſolutio ſecunda. </s>
  <s xml:id="echoid-s2910" xml:space="preserve">Cum prior modus, etſi accuratior et <lb/>perfectior, tamen baſium et perpendiculorum inuentio-<lb/>nem, et ipſam deſcriptionem ueſtigii ſpecuum laborioſis-<lb/>ſimam efficiat, excogitarunt menſores alium, qui circulis <lb/>horariis, quos §. </s>
  <s xml:id="echoid-s2911" xml:space="preserve">39. </s>
  <s xml:id="echoid-s2912" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s2913" xml:space="preserve">laudauimus, abſoluitur. </s>
  <s xml:id="echoid-s2914" xml:space="preserve">Nimirum</s>
</p>
<note position="left" xml:space="preserve">Figur. 16.</note>
<p>
  <s xml:id="echoid-s2915" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2916" xml:space="preserve">Sicuti antea ope compaſſi quaere primi funiculi <lb/>directionem.</s>
  <s xml:id="echoid-s2917" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2918" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2919" xml:space="preserve">In fine illius funiculi, ſuper ligno transuerſario po-<lb/>ne horizontali ſitu circulum horarium, et funiculum cum <lb/>altero, qui per centrum circuli ducitur, connecte; </s>
  <s xml:id="echoid-s2920" xml:space="preserve">tum <lb/>uolue circulum, donec funis horam attingat, quam com-<lb/>
<anchor type="note" xlink:label="note-0172-02a" xlink:href="note-0172-02"/>
paſſus indicauerat; </s>
  <s xml:id="echoid-s2921" xml:space="preserve">ſit funiculus primus a b accurate a meri-<lb/>die in ſeptentrionem ductus, nota igitur in pugillaribus <lb/>h. </s>
  <s xml:id="echoid-s2922" xml:space="preserve">12. </s>
  <s xml:id="echoid-s2923" xml:space="preserve">Se. </s>
  <s xml:id="echoid-s2924" xml:space="preserve">et ita orbem horarium cochleis ligno affige.</s>
  <s xml:id="echoid-s2925" xml:space="preserve"/>
</p>
<div xml:id="echoid-div110" type="float" level="2" n="2">
<note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">Figur. 18.</note>
</div>
<p>
  <s xml:id="echoid-s2926" xml:space="preserve">3. </s>
  <s xml:id="echoid-s2927" xml:space="preserve">Quaere eiusdem funis angulum inclinationis, quem <lb/>libella definiet.</s>
  <s xml:id="echoid-s2928" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2929" xml:space="preserve">4. </s>
  <s xml:id="echoid-s2930" xml:space="preserve">Relinque fixum circulum, et funem tolle, eiusque <lb/>extremum annulum annecte unco, qui prope centrum cir-<lb/>culi eſt, et eundem funem ſecundum ſequentis ſpecus <lb/>axem, quousque libet, profe@@. </s>
  <s xml:id="echoid-s2931" xml:space="preserve">Vbi commode funis fini-<lb/>tur, in ligno iterum pone horizontalem alium circulum <lb/>horarium, e, et eum ſic diſpone, ut linea bcef ſecet ar-<lb/>cum fs, aequalem arcui ſc, h. </s>
  <s xml:id="echoid-s2932" xml:space="preserve">e. </s>
  <s xml:id="echoid-s2933" xml:space="preserve">ut parallelum poſitum <lb/>habeant diametri duorum circulorum (§. </s>
  <s xml:id="echoid-s2934" xml:space="preserve">59. </s>
  <s xml:id="echoid-s2935" xml:space="preserve">62. </s>
  <s xml:id="echoid-s2936" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s2937" xml:space="preserve">et hoc <lb/>ſitu ſtabilem orbem ſecundum redde. </s>
  <s xml:id="echoid-s2938" xml:space="preserve">Ita notare poteris <lb/>arcum ſc in pagillaribus, qui dabit funiculi ſecundi dire-<lb/>ctionem. </s>
  <s xml:id="echoid-s2939" xml:space="preserve">Cuius deinceps inclinatio libella indagatur.</s>
  <s xml:id="echoid-s2940" xml:space="preserve"/>
</p>
<pb o="57" file="0173" n="178" rhead="GEOMETRIA SVBTERRANEA."/>
<p>
  <s xml:id="echoid-s2941" xml:space="preserve">5. </s>
  <s xml:id="echoid-s2942" xml:space="preserve">Aufer priorem circulum b, et in tertiam cauernam <lb/>procede, et ſimiliter quaere directionem funis eh, et ſingu-<lb/>las horas notatas ſolito more in indicem ſcribe, una inue-<lb/>ſtigata inclinatione ad horizontem.</s>
  <s xml:id="echoid-s2943" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2944" xml:space="preserve">6. </s>
  <s xml:id="echoid-s2945" xml:space="preserve">Quoniam autem ſemper horizontali ſitu orbes ho-<lb/>rarii poni debent, ſiquidem lineae plagarum mundi, funt <lb/>radii horizontis ſenſibilis, (§. </s>
  <s xml:id="echoid-s2946" xml:space="preserve">19. </s>
  <s xml:id="echoid-s2947" xml:space="preserve">aſtron. </s>
  <s xml:id="echoid-s2948" xml:space="preserve">ſphaer.) </s>
  <s xml:id="echoid-s2949" xml:space="preserve">attamen <lb/>in ualde inclinatis, cadentibus v. </s>
  <s xml:id="echoid-s2950" xml:space="preserve">g. </s>
  <s xml:id="echoid-s2951" xml:space="preserve">ſpecubus, cum funi-<lb/>culus ex centro circuli, per eius ſuperficiem, trahi commo-<lb/>de nequit, ea propter relinque funem ſecundum directio-<lb/>nem ſpecus porrectum, et ſupra eum circulum horizonta-<lb/>lem fige, ut centrum eiusdem funi immineat, deinceps <lb/>perpendiculum, in funem apice ſuo cadens, iuxta circuli <lb/>peripheriam, demitte, et nota in peripheria horam uel ho-<lb/>rae partem, quam perpendiculi filum ſtringit, eamque ha-<lb/>be pro angulo conuerſionis funiculi in mundi partem. </s>
  <s xml:id="echoid-s2952" xml:space="preserve">nam <lb/>linea illius plagae horizontalis, ex centro orbis educta, per <lb/>filum perpendiculi eſſet tranſitura. </s>
  <s xml:id="echoid-s2953" xml:space="preserve">Pari ratione operare <lb/>in ſpecubus ſurgentibus.</s>
  <s xml:id="echoid-s2954" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2955" xml:space="preserve">7. </s>
  <s xml:id="echoid-s2956" xml:space="preserve">De modo, in charta repraeſentandi ſpecuum ita <lb/>menſuratorum axes, infra agetur.</s>
  <s xml:id="echoid-s2957" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div112" type="section" level="1" n="80">
<head xml:id="echoid-head99" xml:space="preserve">SCHOLION I.</head>
<p>
  <s xml:id="echoid-s2958" xml:space="preserve">55. </s>
  <s xml:id="echoid-s2959" xml:space="preserve">Hanc metiendi fodinas praxin germani uocant, das abziehen <lb/>derer Gebäude, item den Gruben-Zug.</s>
  <s xml:id="echoid-s2960" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div113" type="section" level="1" n="81">
<head xml:id="echoid-head100" xml:space="preserve">SCHOLION II.</head>
<p>
  <s xml:id="echoid-s2961" xml:space="preserve">56. </s>
  <s xml:id="echoid-s2962" xml:space="preserve">Ut modus inſcribondi in indices numeros angulorum, funicu-<lb/>lorum, horarum, una cum eorundem reſolutione, clarius in-<lb/>telligatur, non abs re uidetur, peculiari problemate de hoc argu-<lb/>mento agere.</s>
  <s xml:id="echoid-s2963" xml:space="preserve"/>
</p>
<pb o="58" file="0174" n="179" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div114" type="section" level="1" n="82">
<head xml:id="echoid-head101" xml:space="preserve">DEFINITIO XVII.</head>
<p>
  <s xml:id="echoid-s2964" xml:space="preserve">57. </s>
  <s xml:id="echoid-s2965" xml:space="preserve">Reſolutio numerorum in fodinis inuentorum, (Reſol-<lb/>virung des Gruben-Zugs) nominatur artificium, <lb/>quo, pro hypotenuſis et angulis datis, perpendicula et baſes <lb/>quaeruntur, et una cum ſuis angulis in peculiari indice <lb/>ordinantur.</s>
  <s xml:id="echoid-s2966" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div115" type="section" level="1" n="83">
<head xml:id="echoid-head102" xml:space="preserve">PROBLEMA V.</head>
<p>
  <s xml:id="echoid-s2967" xml:space="preserve">58. </s>
  <s xml:id="echoid-s2968" xml:space="preserve">Reſolutionem numerorum modo explicatam rite peragere.</s>
  <s xml:id="echoid-s2969" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2970" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s2971" xml:space="preserve">Quemadmodum exemplum hic pro-<lb/>poſitum docet, fiant claſſes titulis ſuis diſtinctae, et ex ta-<lb/>bulis perpendiculorum et baſium, eo modo quem ſupra <lb/>§. </s>
  <s xml:id="echoid-s2972" xml:space="preserve">48. </s>
  <s xml:id="echoid-s2973" xml:space="preserve">copioſius tradidi, pro hypotenuſis et angulis, iſta per-<lb/>pendicula et baſes quaerantur, et cum numeris reſponden-<lb/>tibus comparentur, inprimis uero perpendicula ſpecuum <lb/>cadentium et ſurgentium diſtinguantur, ita reſolutio quae-<lb/>ſita abſoluetur.</s>
  <s xml:id="echoid-s2974" xml:space="preserve"/>
</p>
<pb o="59" file="0175" n="180" rhead="GEOMETRIA SVBTERRANEA."/>
<note position="right" xml:space="preserve"> <lb/># # # # # # # 8 Bafes # 9 Catheti furgentium. # 10 Catheti cadentium. <lb/>1. Loca mundi. # 2. Cad. et ſurgent. # 3. Gradus libellae. # 4. Uln. er 8uae funic. # 5. Digiti # 6. Horae Compaſſi. # 7. Octau. p. hor. # Ulnae # Octauae # Digiti # Ulnae # Octauae # Digiti # Ulnae # Octauae # Digiti # 11. Signa # 12. Annotationes <lb/>- # Surg. # 90 # {1/2} # - # - # - # - # - # - # - # 4 # - # - # - # - # - # diſtantia puncti <lb/>prenſionis ab hori-<lb/>zontali. <lb/>SE. # cad. # 1 # 4 # - # 1 # 7 {1/4} # 3 # 7 # 9 # - # - # - # - # - # 55 # -<lb/>OR. # c. # 4 # 1 {1/2} # - # 3 # 3 {1/2} # 1 # 3 # 9 # - # - # - # - # - # 82 # -<lb/>SE. # c. # 1 # 4 {3/4} # 4 # 1 # 2 {3/4} # 4 # 6 # 3 # - # - # - # - # - # 65 # -<lb/>SE. # c. # {1/4} # 4 {3/4} # - # 12 # 5 {1/2} # 4 # 6 # - # - # - # - # - # - # 15 # - # hinc fub dift. 2 {5/8} <lb/>Uln. et ſub h. 6. <lb/>uena transuerſa. <lb/>SE. # c. # 1 # 2 {1/4} # - # 2 # 4 {1/4} # 2 # - # 9 # - # - # - # - # - # 30 # - # hinc fub diſt. {3/4} <lb/>Uln. et fub h. 10 {1/2} <lb/>uena tranſit. <lb/>OR. # ſ. # {1/4} # 6 # 4 # 3 # 4 {1/4} # 6 # - # - # - # - # 20 # - # - # - # -<lb/>OR. # c. # 4 # 3 {1/2} # - # 3 # 5 {1/4} # 3 # 3 # 9 # - # - # - # - # 1 # 94 # -<lb/>OR. # c. # 1 {1/2} # 6 # 3 # 3 # 1 {1/4} # 6 # - # 2 # - # - # - # - # 1 # 25 # -<lb/>OR. # c. # 4 {1/4} # 5 # 3 # 3 # 2 {1/4} # 5 # - # 2 # - # - # - # - # 2 # 98 # -<lb/>OR. # - # - # 5 # 5 # 3 # 7 {3/4} # 5 # - # 5 # - # - # - # - # - # - # -<lb/>OR. # c. # 2 {1/4} # 2 # 3 # 3 # 1 # 2 # - # 2 # - # - # - # - # - # 62 # -<lb/>OR. # - # - # 2 {7/8} # - # 3 # 4 {1/4} # 2 # 7 # - # - # - # - # - # - # - # -<lb/>SE. # c. # {3/4} # 2 {1/8} # 3 # 1 # 4 # 2 # 1 # 2 # - # - # - # - # 1 # 39 # † # usque ad parietern <lb/>oſtii cuniculi (Stol-<lb/>lens Mundloch) <lb/>usque ad lineam <lb/>horizontalem <lb/># c. # 90 # {3/4} # 8 # - # - # - # - # - # - # - # - # - # 6 # 80 # -<lb/># # # # # # # # # # - # 4 # 20 # 2 # 1 # 45 # -<lb/></note>
<pb o="60" file="0176" n="181" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div116" type="section" level="1" n="84">
<head xml:id="echoid-head103" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s2975" xml:space="preserve">59. </s>
  <s xml:id="echoid-s2976" xml:space="preserve">Ex hoc ſyllabo apparet 1) quod ubi nullus libellae angulus indi-<lb/>catur, linea ſit horizontalis. </s>
  <s xml:id="echoid-s2977" xml:space="preserve">2) cathetum ſurgentium ſpe-<lb/>cuum, utpote minorem, ſubtractum a catheto cadentium, relinquere <lb/>1 {5/8} Uln. </s>
  <s xml:id="echoid-s2978" xml:space="preserve">2. </s>
  <s xml:id="echoid-s2979" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s2980" xml:space="preserve">pro caſu, ſiue pro perpendiculari diſtantia ſuperficiei <lb/>aquae a linea horizontali per extremum cuniculi oſtium producta.</s>
  <s xml:id="echoid-s2981" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div117" type="section" level="1" n="85">
<head xml:id="echoid-head104" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s2982" xml:space="preserve">60. </s>
  <s xml:id="echoid-s2983" xml:space="preserve">Quia eorum, quae circa fodinarum dimenſionem et compara-<lb/>tionem neceſſaria ſunt, inuentio ſine ichnographia fieri nequit, <lb/>de ea ut nunc explicetur, ordo iubet.</s>
  <s xml:id="echoid-s2984" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div118" type="section" level="1" n="86">
<head xml:id="echoid-head105" xml:space="preserve">DEFINITIO XIIX.</head>
<p>
  <s xml:id="echoid-s2985" xml:space="preserve">61. </s>
  <s xml:id="echoid-s2986" xml:space="preserve">Ichnographia eſt deſcriptio ueſtigii ſpecuum ſubterraneo-<lb/>rum, ſiue areae, in quam meatus huc illuc reflexi, et <lb/>horizontaliſitu repraeſentati, diffunduntur.</s>
  <s xml:id="echoid-s2987" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div119" type="section" level="1" n="87">
<head xml:id="echoid-head106" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s2988" xml:space="preserve">62. </s>
  <s xml:id="echoid-s2989" xml:space="preserve">Putei igitur perpendicularis ueſtigium oſtium praebet, <lb/>atque ſic etiam delineatur.</s>
  <s xml:id="echoid-s2990" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div120" type="section" level="1" n="88">
<head xml:id="echoid-head107" xml:space="preserve">PROBLEMA VI.</head>
<p style="it">
  <s xml:id="echoid-s2991" xml:space="preserve">63. </s>
  <s xml:id="echoid-s2992" xml:space="preserve">Icbnographiam fodinarum, in quibus compaſſus adbibitus fuit, <lb/>delineare.</s>
  <s xml:id="echoid-s2993" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s2994" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s2995" xml:space="preserve">1. </s>
  <s xml:id="echoid-s2996" xml:space="preserve">Reſolue dimenſiones in ſpecubus ca-<lb/>ptas, et perpendicula ac baſes@quaere pro hypotenuſis, et <lb/>in tabulas refer. </s>
  <s xml:id="echoid-s2997" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s2998" xml:space="preserve">59.)</s>
  <s xml:id="echoid-s2999" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3000" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3001" xml:space="preserve">In tabula horizontali pone et cera affige folium <lb/>chartae.</s>
  <s xml:id="echoid-s3002" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3003" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3004" xml:space="preserve">Compaſſum inſere inſtrumento lineationis, et <lb/>
<anchor type="note" xlink:label="note-0176-01a" xlink:href="note-0176-01"/>
idem ita diſpone, ut primae lineae horam bc indicet, de-<lb/>inde duc ceruſſa iuxta latera inſtrumenti lineam obſcuram, <lb/>et eius magnitudinem ſcala menſuratam defini;</s>
  <s xml:id="echoid-s3005" xml:space="preserve"/>
</p>
<div xml:id="echoid-div120" type="float" level="2" n="1">
<note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">Figur. 10.</note>
</div>
<pb o="61" file="0177" n="182" rhead="GEOMETRIA SVBTERRANEA."/>
<p>
  <s xml:id="echoid-s3006" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3007" xml:space="preserve">Similiter ſecundum angulos reſpondentes delinea <lb/>bafes reliquas, et deinceps ductibus parallelis meatuum la-<lb/>titudines repraeſenta, et poſtquam ceruſſa feciſti prima fi-<lb/>gurae lineamenta, tum etiam diſtinctius lineis atramento <lb/>fignatis eadem deſcribe.</s>
  <s xml:id="echoid-s3008" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3009" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3010" xml:space="preserve">Illud per ſe perſpicuum eſt, ſemper compaſſi l@-<lb/>cum S, prorſum, uti in fodina factum eſt, uertendum eſſe.</s>
  <s xml:id="echoid-s3011" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3012" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3013" xml:space="preserve">Adde figurae ſigna in fodinis obſeruata, et ſpecuum <lb/>transuerſariorum loca, et appinge ſcalam, qua baſes es di-<lb/>menſus.</s>
  <s xml:id="echoid-s3014" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3015" xml:space="preserve">Exemplum talis ichnographiae, inſtrumento lineationis, <lb/>ad ductum numerorum §. </s>
  <s xml:id="echoid-s3016" xml:space="preserve">58. </s>
  <s xml:id="echoid-s3017" xml:space="preserve">laudatorum factae, exhibet <lb/>Figura 20.</s>
  <s xml:id="echoid-s3018" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div122" type="section" level="1" n="89">
<head xml:id="echoid-head108" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3019" xml:space="preserve">64. </s>
  <s xml:id="echoid-s3020" xml:space="preserve">Praecipiunt menſores, ut eodem, quo menſiones captae ſunt <lb/>loco, u.</s>
  <s xml:id="echoid-s3021" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3022" xml:space="preserve">intra aedes fodinae uicinas, ichnographia abſolua-<lb/>tur, ne quando longius diſceſſum inde eſt, turbet pragmatiam mu-<lb/>tata acus magneticae declinatio.</s>
  <s xml:id="echoid-s3023" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div123" type="section" level="1" n="90">
<head xml:id="echoid-head109" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s3024" xml:space="preserve">65. </s>
  <s xml:id="echoid-s3025" xml:space="preserve">Quando compaſſo iacente in fodinis geometra uſus eſt, <lb/>eodem etiam ichnographia ſimili fere modo fit. </s>
  <s xml:id="echoid-s3026" xml:space="preserve">Si-<lb/>quidem baſes inuentae ſecundum eosdem in charta angulos <lb/>diſponuntur, quos hypotenuſae ſpecuum interceperunt.</s>
  <s xml:id="echoid-s3027" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div124" type="section" level="1" n="91">
<head xml:id="echoid-head110" xml:space="preserve">PROBLEMA VII.</head>
<p style="it">
  <s xml:id="echoid-s3028" xml:space="preserve">66. </s>
  <s xml:id="echoid-s3029" xml:space="preserve">Ichnographiam ferrifodinarum deſcribere.</s>
  <s xml:id="echoid-s3030" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3031" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3032" xml:space="preserve">Caſus primus, quando ſolis funiculis di-<lb/>
<anchor type="note" xlink:label="note-0177-01a" xlink:href="note-0177-01"/>
rectio ſpecuum menſurata eſt. </s>
  <s xml:id="echoid-s3033" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s3034" xml:space="preserve">54. </s>
  <s xml:id="echoid-s3035" xml:space="preserve">n. </s>
  <s xml:id="echoid-s3036" xml:space="preserve">1.)</s>
  <s xml:id="echoid-s3037" xml:space="preserve"/>
</p>
<div xml:id="echoid-div124" type="float" level="2" n="1">
<note position="right" xlink:label="note-0177-01" xlink:href="note-0177-01a" xml:space="preserve">Figur. 9.</note>
</div>
<p>
  <s xml:id="echoid-s3038" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3039" xml:space="preserve">Quia primae lineae ſitus compaſſi beneficio inno-<lb/>tuit, eadem inftrumento lineationis, in charta ſcribitur, et <lb/>pro baſeos magnitudine definitur.</s>
  <s xml:id="echoid-s3040" xml:space="preserve"/>
</p>
<pb o="62" file="0178" n="183" rhead="GEOMETRIA SVBTERRANEA."/>
<p>
  <s xml:id="echoid-s3041" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3042" xml:space="preserve">Verum, pro inueniendo flexu ſequentis lineae be, <lb/>
<anchor type="note" xlink:label="note-0178-01a" xlink:href="note-0178-01"/>
haec monita obſeruanda ſunt. </s>
  <s xml:id="echoid-s3043" xml:space="preserve">Scilicet ſit triangulum cbd <lb/>horizontaliter exhibendum, ſeparata figura propoſitum. <lb/></s>
  <s xml:id="echoid-s3044" xml:space="preserve">ex ea apparet, lineas cb, bd, cd, ſingulas habere ſua perpen-<lb/>dicula et baſes, quae angulis inclinationis competunt. </s>
  <s xml:id="echoid-s3045" xml:space="preserve">et ſi <lb/>infima horizontalis zyd, ducatur, et catheti by, cz demit-<lb/>tantur, erit perpendiculum bx illud, quod hypotenuſae cb <lb/>debetur, alterum by eſt pro funiculo bd, tertium cz pro <lb/>fune cd et quia cx, zy ſunt parallelae, erit cz = xy <lb/>(§. </s>
  <s xml:id="echoid-s3046" xml:space="preserve">16. </s>
  <s xml:id="echoid-s3047" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s3048" xml:space="preserve">eſt autem xy = by - bx, ex quo fluit mo-<lb/>dus, reperiundi baſin zd; </s>
  <s xml:id="echoid-s3049" xml:space="preserve">nempe quaerantur catheti funium <lb/>cb, bd, et ſumatur eorum differentia = xy = cz porro <lb/>data hypotenuſa cd, numeris definita, quadratum eius-<lb/>dem ſumatur, et a ן cd dematur ן cz, et ſupererit ן zd <lb/>(§. </s>
  <s xml:id="echoid-s3050" xml:space="preserve">148. </s>
  <s xml:id="echoid-s3051" xml:space="preserve">Geom.) </s>
  <s xml:id="echoid-s3052" xml:space="preserve">extractaque radice, (§. </s>
  <s xml:id="echoid-s3053" xml:space="preserve">98. </s>
  <s xml:id="echoid-s3054" xml:space="preserve">Arith.) </s>
  <s xml:id="echoid-s3055" xml:space="preserve">ipſa ba-<lb/>ſis zd noteſcet. </s>
  <s xml:id="echoid-s3056" xml:space="preserve">Cognitis baſibus, triangulum cbd com-<lb/>ponatur, et linea be ducatur, quae ſuniculi ſequentis, in <lb/>fodina inuenti, baſi aequalis eſt. </s>
  <s xml:id="echoid-s3057" xml:space="preserve">et fimiliter, his ſequentium <lb/>angulorum determinatio inſtituatur.</s>
  <s xml:id="echoid-s3058" xml:space="preserve"/>
</p>
<div xml:id="echoid-div125" type="float" level="2" n="2">
<note position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">Figur. 10.</note>
</div>
<p>
  <s xml:id="echoid-s3059" xml:space="preserve">Caſus ſecundus, quando circuli horarii in ſpecubus fue-<lb/>runt adhibiti.</s>
  <s xml:id="echoid-s3060" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3061" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3062" xml:space="preserve">Iterum baſeos primi funiculi poſitio compaſſo no-<lb/>tata, inſtrumento lineationis ſignetur.</s>
  <s xml:id="echoid-s3063" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3064" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3065" xml:space="preserve">ſequentes ductus facili opera transportatorio circu-<lb/>lari, annectuntur. </s>
  <s xml:id="echoid-s3066" xml:space="preserve">nempe applicatur illius centrum extre-<lb/>mo primae baſeos, et mouetur ille orbis, donec prior li-<lb/>nea peripheriae circularis @unctum in pugillaribus ſcri-<lb/>ptum indicat. </s>
  <s xml:id="echoid-s3067" xml:space="preserve">tum reſpicitur etiam angulus funiculi ſe-<lb/>quentis, et prope orbem horarium reſpondens punctum <lb/>ceruſſa uel ſtili apice in charta deſignatur; </s>
  <s xml:id="echoid-s3068" xml:space="preserve">deinceps ex <lb/>centro per hoc punctum linea producitur, et magnitudo <lb/>baſeos, ex ſcala accepta reſecatur. </s>
  <s xml:id="echoid-s3069" xml:space="preserve">Eodem modo reliquae <lb/>quoque baſes componuntur.</s>
  <s xml:id="echoid-s3070" xml:space="preserve"/>
</p>
<pb o="63" file="0179" n="184" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div127" type="section" level="1" n="92">
<head xml:id="echoid-head111" xml:space="preserve">DEFINITIO XIX.</head>
<p>
  <s xml:id="echoid-s3071" xml:space="preserve">67. </s>
  <s xml:id="echoid-s3072" xml:space="preserve">Menſio ſubdialis (der Tage - Zug) uocatur praxis, qua <lb/>linearum ſupra terram, ſiue in ſuperficie terrae ex-<lb/>tenſarum, ſitus, tum qua inclinationem ad horizontem, <lb/>tum qua conuerſionem ad plagas mundi, inueſtigatur et <lb/>definitur.</s>
  <s xml:id="echoid-s3073" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div128" type="section" level="1" n="93">
<head xml:id="echoid-head112" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s3074" xml:space="preserve">68. </s>
  <s xml:id="echoid-s3075" xml:space="preserve">Itaque in hac quoque dimenſione libella, et compaſſus <lb/>officium ſuum facient, ſi ex goniodicte baculo impoſito, <lb/>ſuſpendantur.</s>
  <s xml:id="echoid-s3076" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div129" type="section" level="1" n="94">
<head xml:id="echoid-head113" xml:space="preserve">PROBLEMA VII.</head>
<p>
  <s xml:id="echoid-s3077" xml:space="preserve">69. </s>
  <s xml:id="echoid-s3078" xml:space="preserve">Menſionem ſubdialem inſtituere.</s>
  <s xml:id="echoid-s3079" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3080" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3081" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3082" xml:space="preserve">Eligatur tempus, quo aer tranquil-<lb/>lus eſt, ut in libella perpendiculum, et in compaſſo acus, <lb/>accurate optatas circulorum partes deſignent. </s>
  <s xml:id="echoid-s3083" xml:space="preserve">Tale autem <lb/>tempus plerumque matutinum exiſtit.</s>
  <s xml:id="echoid-s3084" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3085" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3086" xml:space="preserve">Praeparetur in pugillaribus tabula, pro numeris <lb/>inſcribendis, qualis ſupra §. </s>
  <s xml:id="echoid-s3087" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3088" xml:space="preserve">n. </s>
  <s xml:id="echoid-s3089" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3090" xml:space="preserve">praeſcripta eſt.</s>
  <s xml:id="echoid-s3091" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3092" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3093" xml:space="preserve">funiculus aſſumatur 6 uel 10 ulnarum, uel ſaltem <lb/>non multo maior, alias enim pondere ſuo, poſtquam extre-<lb/>mis in baculis annexus eſt, nimium trahitur, et curuatur. <lb/></s>
  <s xml:id="echoid-s3094" xml:space="preserve">Quin mihi uidetur quoque conſultum, praeter funem ca-<lb/>tenam adhibere, et eadem longitudinem funiculi, metiri, <lb/>ſi forte eius contractionem, quae in ſolo, pruinis aut rore <lb/>madido, cito contingere ſolet, ſufpicari poſſis. </s>
  <s xml:id="echoid-s3095" xml:space="preserve">Debet au-<lb/>tem funis in extremis annulos habere, in quos baculorum <lb/>ſumma immittantur.</s>
  <s xml:id="echoid-s3096" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3097" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3098" xml:space="preserve">alligetur in principio lineae, v.</s>
  <s xml:id="echoid-s3099" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3100" xml:space="preserve">in ſummo putei <lb/>funiculus, tum recta procedatur eo, quo linea menſuranda <lb/>porrigitur, et quando funis eſt 6 ulnarum, tanto interuallo a
<pb o="64" file="0180" n="185" rhead="GEOMETRIA SVBTERRANEA."/>
principio baculus ſtatuatur, et funiculi tenſi annulus eidem <lb/>imponatur.</s>
  <s xml:id="echoid-s3101" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3102" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3103" xml:space="preserve">Suſpendatur ex fune libra, et poſtea etiam com-<lb/>paſſus penſilis, prorſum conuerſo ſeptentrionis ſigno, et <lb/>in indicem referantur, gradus libellae, hora compaſſi, una <lb/>cum longitudine funis.</s>
  <s xml:id="echoid-s3104" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3105" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3106" xml:space="preserve">Ita pergendo, donec ad extremum lineae peruenia-<lb/>tur, facta erit menſio ſubdialis.</s>
  <s xml:id="echoid-s3107" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3108" xml:space="preserve">7. </s>
  <s xml:id="echoid-s3109" xml:space="preserve">Seruatur autem funiculi longitudo eadem, tum quia <lb/>plerumque in patente campo licet, tum quia ad calculum <lb/>facilitandum conducit. </s>
  <s xml:id="echoid-s3110" xml:space="preserve">Si uero areae conditio non pati-<lb/>tur eandem funiculi magnitudinem, alia quoque pro lubi-<lb/>tu aſſumi poteſt, modo diligenter ulnae in pugillaribus an-<lb/>notentur.</s>
  <s xml:id="echoid-s3111" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div130" type="section" level="1" n="95">
<head xml:id="echoid-head114" xml:space="preserve">PROBLEMA IX.</head>
<p style="it">
  <s xml:id="echoid-s3112" xml:space="preserve">70. </s>
  <s xml:id="echoid-s3113" xml:space="preserve">Menſionis ſubdialis ichnographiam facere.</s>
  <s xml:id="echoid-s3114" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3115" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3116" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3117" xml:space="preserve">Reſoluatur prius menſio ſupra ter-<lb/>ram facta, et baſes funibus et angulis debiti inueniantur.</s>
  <s xml:id="echoid-s3118" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3119" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3120" xml:space="preserve">Eodem modo, quo ſpecuum ſubterraneorum ueſti-<lb/>gia delineata ſunt, etiam flexus baſium, menſionis in ſuper-<lb/>ficie telluris peractae, deſcribantur, et erit ichnographia <lb/>quaeſita abſoluta.</s>
  <s xml:id="echoid-s3121" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div131" type="section" level="1" n="96">
<head xml:id="echoid-head115" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3122" xml:space="preserve">71. </s>
  <s xml:id="echoid-s3123" xml:space="preserve">Exemplum tale eſto. </s>
  <s xml:id="echoid-s3124" xml:space="preserve">Scire cupio, quantum ab oſtio cuniculi <lb/>
<anchor type="note" xlink:label="note-0180-01a" xlink:href="note-0180-01"/>
b usque ad locum i, unde puteus ad eundem cuniculum de-<lb/>mittendus eſt, ſurgat terrae ſuperſicies. </s>
  <s xml:id="echoid-s3125" xml:space="preserve">id manifeſtabit menſio ſu-<lb/>perterranea, prout numeri cum reſolutione ſequente tabula refe-<lb/>runt: </s>
  <s xml:id="echoid-s3126" xml:space="preserve">et iisdem accommodata eſt figura 2@. </s>
  <s xml:id="echoid-s3127" xml:space="preserve">in qua baſes inuentas, <lb/>beneficio inſirumenti lineationis et ſcalae geometricae, compoſui.</s>
  <s xml:id="echoid-s3128" xml:space="preserve"/>
</p>
<div xml:id="echoid-div131" type="float" level="2" n="1">
<note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">Figur. 20.</note>
</div>
<pb o="65" file="0181" n="186" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div133" type="section" level="1" n="97">
<head xml:id="echoid-head116" xml:space="preserve">Menſio ſubdialis reſoluta.</head>
<note position="right" xml:space="preserve"> <lb/># # # # # # # 8 Baſes # 9 Catheti ſurgentium. # 10 Catheti cadentium. # Fig. 20. <lb/>1. Loca Mundi. # 2. Cad. et ſurgent. # 3. Gradus librae. # 4. Uln. et 8uae # 5. Digiti # 6. Horae Compaſſi. # 7. Octau. hor. # Ulnae # Octauae # Digiti # Ulnae # Octauae # Digiti # Ulnae # Octauae # Digiti # 11. Signa # 12. Annotationis <lb/>- # ſ. # 90 # {3/4} # 8 # - # - # - # - # - # - # 6 # 80 # - # - # - # - # a lin. horiz. ad <lb/>punct. prehenſi-<lb/>onis. <lb/>ME. # ſ. # @9 {1/2} # 1 {3/4} # - # 12 # {1/4} # 1 # 4 # 1 # - # 6 # 88 # - # - # - # - # ufq. ad palum <lb/>primum c. <lb/>OC. # ſ. # 5 {1/4} # 10 {5/8} # 2 # 3 # {3/4} # 10 # 4 # 8 # - # 7 # 78 # - # - # - # - # ad palum d. <lb/>OC. # ſ. # 4 {1/2} # 10 {5/8} # 3 # 3 # 5 # 10 # 5 # - # - # 6 # 67 # - # - # - # - # ad palum e. <lb/>OC. # ſ. # 9 # 10 {3/8} # 6 # 3 # {3/4} # 10 # 2 # 5 # 2 # 1 # 56 # - # - # - # - # ad palum f. <lb/>ME. # ſ. # 4 {1/4} # 10 {1/2} # 8 # 2 # 2 # 10 # 4 # 5 # - # 6 # 26 # - # - # - # - # ad palum g. <lb/>ME. # ſ. # 6 {1/4} # 10 {1/2} # 7 # 2 # 2 # 10 # 4 # 2 # 1 # 1 # 20 # - # - # - # - # ad palum h. <lb/>ME. # ſ. # 7 # 9 {1/8} # 5 # 2 # 4 {1/4} # 9 # - # 9 # 1 # - # 90 # - # - # - # - # ad palum ſept. &amp; <lb/>ult. i. ſiue ad ma-<lb/>chinam tractori-<lb/>am puteo immi-<lb/>nentem. <lb/># # # # # # # # # # - # - # -<lb/># # # # # # # # # # 8 # 6 # 05 <lb/>S. # c. # 77 # 3 {3/4} # 5 # 11 # 5 # - # 6 # 8 # - # - # - # 3 # 5 # 69 # - # Hinc in ipſum pu-<lb/>teuna perrectum <lb/>eſt. <lb/># c. # 90 # {1/2} # 5 # - # - # - # - # - # - # - # - # - # 4 # 50 # -<lb/># # # # # # # # # # # # # - # - # -<lb/># # # # # # # # # # # # # 4 # 2 # 19 <lb/></note>
<pb o="66" file="0182" n="187" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div134" type="section" level="1" n="98">
<head xml:id="echoid-head117" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s3129" xml:space="preserve">72. </s>
  <s xml:id="echoid-s3130" xml:space="preserve">Facta cathetorum additione, apparet, ſuperficiem terrae <lb/>ab oſtio cuniculi usque ad puteum i ſurgere 8 Uln. <lb/></s>
  <s xml:id="echoid-s3131" xml:space="preserve">6 octau. </s>
  <s xml:id="echoid-s3132" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s3133" xml:space="preserve">{3/4}, et quia ſupra §. </s>
  <s xml:id="echoid-s3134" xml:space="preserve">59. </s>
  <s xml:id="echoid-s3135" xml:space="preserve">notatum eſt, diſtantiam ho-<lb/>rizontalium per punctum oſtii extremi, et per principium di-<lb/>menſionis, ductarum, eſſe 1 {5/8} Uln. </s>
  <s xml:id="echoid-s3136" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3137" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s3138" xml:space="preserve">dum puteus teſte §. </s>
  <s xml:id="echoid-s3139" xml:space="preserve"><lb/>praec. </s>
  <s xml:id="echoid-s3140" xml:space="preserve">altitudinem 4 {1/4} Uln. </s>
  <s xml:id="echoid-s3141" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3142" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s3143" xml:space="preserve">habet, ſequitur, ſupereſſe, <lb/>2 {3/4} Uln. </s>
  <s xml:id="echoid-s3144" xml:space="preserve">7. </s>
  <s xml:id="echoid-s3145" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s3146" xml:space="preserve">per quam lineam puteus debet continuari, ut <lb/>horizontalem cuniculi attingat.</s>
  <s xml:id="echoid-s3147" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div135" type="section" level="1" n="99">
<head xml:id="echoid-head118" xml:space="preserve">PROBLEMA X.</head>
<p style="it">
  <s xml:id="echoid-s3148" xml:space="preserve">73. </s>
  <s xml:id="echoid-s3149" xml:space="preserve">Inuenire altitudinem perpendicularem loci alicuius ſubter ter-<lb/>ram, uel a terrae ſuperficie, uel ab alio loco ſubterraneo.</s>
  <s xml:id="echoid-s3150" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3151" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3152" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3153" xml:space="preserve">Quando in menſione fodinarum ſurgen-<lb/>tes et cadentes ſpecus miſcentur, accipe utriusque generis, <lb/>nempe ſurgentium et cadentium, ſummas, et minorem a <lb/>maiore aufer, reſiduum monſtrabit altitudinem, uel depres-<lb/>ſionem perpendicularem, unius loci prae altero.</s>
  <s xml:id="echoid-s3154" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3155" xml:space="preserve">v.</s>
  <s xml:id="echoid-s3156" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3157" xml:space="preserve">in noſtro exemplo §. </s>
  <s xml:id="echoid-s3158" xml:space="preserve">58. </s>
  <s xml:id="echoid-s3159" xml:space="preserve">erat ſumma cathetorum <lb/>ſurgentium 4. </s>
  <s xml:id="echoid-s3160" xml:space="preserve">oct. </s>
  <s xml:id="echoid-s3161" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3162" xml:space="preserve">dig. </s>
  <s xml:id="echoid-s3163" xml:space="preserve">ſed ſumma cadentium eſt 2. </s>
  <s xml:id="echoid-s3164" xml:space="preserve">Uln. <lb/></s>
  <s xml:id="echoid-s3165" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3166" xml:space="preserve">oct. </s>
  <s xml:id="echoid-s3167" xml:space="preserve">4 {5/10} dig. </s>
  <s xml:id="echoid-s3168" xml:space="preserve">ergo facta ſubtractione, relinquitur 1. </s>
  <s xml:id="echoid-s3169" xml:space="preserve">Uln. </s>
  <s xml:id="echoid-s3170" xml:space="preserve"><lb/>5. </s>
  <s xml:id="echoid-s3171" xml:space="preserve">oct. </s>
  <s xml:id="echoid-s3172" xml:space="preserve">2 {5/10} dig. </s>
  <s xml:id="echoid-s3173" xml:space="preserve">pro perpendiculari depreſſione loci primi <lb/>ab ultimo.</s>
  <s xml:id="echoid-s3174" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3175" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3176" xml:space="preserve">Similiter etiam ab alio loco ſubterraneo perpen-<lb/>dicularis diſtantia habetur, ſi, pro ſumma cathetorum <lb/>conſtituenda, inde initium ducatur.</s>
  <s xml:id="echoid-s3177" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3178" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3179" xml:space="preserve">Quod ſi uero diſtantiam a loco ſupra terram ſcire <lb/>deſideres, componatur menſio ſubterranea cum ſubdiali, <lb/>et utriusque perpendicularis aſcenſus uel deſcenſus quae-<lb/>ratur. </s>
  <s xml:id="echoid-s3180" xml:space="preserve">nam etiam horum ſumma uel diſcrimen quaeſitum <lb/>aperiet.</s>
  <s xml:id="echoid-s3181" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3182" xml:space="preserve">v.</s>
  <s xml:id="echoid-s3183" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3184" xml:space="preserve">aſcendat ſuperficies terrae a principio menſio-<lb/>nis ad aliquem puteum 8 {3/4} Uln.</s>
  <s xml:id="echoid-s3185" xml:space="preserve">, ſpecuum uero perpendi-
<pb o="67" file="0183" n="188" rhead="GEOMETRIA SVBTERRANEA."/>
cularis deſcenſus, ab eodem initio uerſus eundem puteum, <lb/>eſt 4. </s>
  <s xml:id="echoid-s3186" xml:space="preserve">Uln. </s>
  <s xml:id="echoid-s3187" xml:space="preserve">ſumma 1 2 {3/4} dabit totam profunditatem a puteo <lb/>ad imi loci lineam horizontalem. </s>
  <s xml:id="echoid-s3188" xml:space="preserve">quando autem aſcendit <lb/>mons, et aſcendit quoque ſpecus usque ad aliquem ter-<lb/>minum, differentia perpendiculorum, dabit altitudinem <lb/>optatam.</s>
  <s xml:id="echoid-s3189" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div136" type="section" level="1" n="100">
<head xml:id="echoid-head119" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3190" xml:space="preserve">74. </s>
  <s xml:id="echoid-s3191" xml:space="preserve">Voigtelius p. </s>
  <s xml:id="echoid-s3192" xml:space="preserve">98. </s>
  <s xml:id="echoid-s3193" xml:space="preserve">uhi de computandis baſibus et perpendiculis, <lb/>quac bypotenuſis et angulis datis competunt, egit, etiam regu-<lb/>lam commendat, pro examine calculi inſtituti, talem: </s>
  <s xml:id="echoid-s3194" xml:space="preserve">ſumatur ſigil-<lb/>latim ſumma baſium, perpendiculorum et bypotenuſarum, ex ſum-<lb/>mis prioribus fiant quadrata, eademque addantur, et ex aggregato <lb/>radix quaeratur, ſi haec aequalis eſt ſummae bypotenuſarum, putat <lb/>recte ſe habere factae menſionis reſolutionem, et ſundamentum huius <lb/>praecepti in theoremate pythagorico quaerit. </s>
  <s xml:id="echoid-s3195" xml:space="preserve">Enimuero pytbagorae <lb/>inuentum, quod ad unum tantum triangulum rectangulum pertinet, <lb/>ad plura et diſſimilia irrito labore trabi, ſequens analytica demon-<lb/>
<anchor type="note" xlink:label="note-0183-01a" xlink:href="note-0183-01"/>
ſtratic euincet. </s>
  <s xml:id="echoid-s3196" xml:space="preserve">Sint triangulorum perpendicula a et c, baſes b et d, <lb/>bypotenuſae x et y, erit</s>
</p>
<div xml:id="echoid-div136" type="float" level="2" n="1">
<note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">Figur. 21. <lb/>Tab. 3.</note>
</div>
<p>
  <s xml:id="echoid-s3197" xml:space="preserve">ן a + c = a<emph style="super">2</emph> + 2 a c + c<emph style="super">2</emph>, et</s>
</p>
<p>
  <s xml:id="echoid-s3198" xml:space="preserve">ן b + d = b<emph style="super">2</emph> + 2 b d + d<emph style="super">2</emph></s>
</p>
<p>
  <s xml:id="echoid-s3199" xml:space="preserve">ן x + y = x<emph style="super">2</emph> + 2 x y + yy (§. </s>
  <s xml:id="echoid-s3200" xml:space="preserve">34. </s>
  <s xml:id="echoid-s3201" xml:space="preserve">Analyſ. </s>
  <s xml:id="echoid-s3202" xml:space="preserve">finit.)</s>
  <s xml:id="echoid-s3203" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3204" xml:space="preserve">et per theor. </s>
  <s xml:id="echoid-s3205" xml:space="preserve">pyth.</s>
  <s xml:id="echoid-s3206" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3207" xml:space="preserve">a<emph style="super">2</emph> + b<emph style="super">2</emph> = x<emph style="super">2</emph></s>
</p>
<p>
  <s xml:id="echoid-s3208" xml:space="preserve">et c<emph style="super">2</emph> + d<emph style="super">2</emph> = y y</s>
</p>
<p>
  <s xml:id="echoid-s3209" xml:space="preserve">extractaque radice</s>
</p>
<p>
  <s xml:id="echoid-s3210" xml:space="preserve">V a<emph style="super">2</emph> + b<emph style="super">2</emph> = x</s>
</p>
<p>
  <s xml:id="echoid-s3211" xml:space="preserve">V c<emph style="super">2</emph> + d<emph style="super">2</emph> = y</s>
</p>
<p>
  <s xml:id="echoid-s3212" xml:space="preserve">et ſecundum bypotheſin praecepti voigteliani foret</s>
</p>
<p>
  <s xml:id="echoid-s3213" xml:space="preserve">a<emph style="super">2</emph> + 2 a c + c<emph style="super">2</emph> + b<emph style="super">2</emph> + 2 b d + d<emph style="super">2</emph> = x<emph style="super">2</emph> + 2xy + yy</s>
</p>
<p>
  <s xml:id="echoid-s3214" xml:space="preserve">ſubſtituto ualore x x et y y</s>
</p>
<p>
  <s xml:id="echoid-s3215" xml:space="preserve">a<emph style="super">2</emph> + 2 a c + c<emph style="super">2</emph> + b<emph style="super">2</emph> + 2bd + d<emph style="super">2</emph> = a<emph style="super">2</emph> + b<emph style="super">2</emph> + 2xy + c<emph style="super">2</emph> + d<emph style="super">2</emph></s>
</p>
<p>
  <s xml:id="echoid-s3216" xml:space="preserve">et aequalibus ablatis,</s>
</p>
<pb o="68" file="0184" n="189"/>
<p style="it">
  <s xml:id="echoid-s3217" xml:space="preserve">2ac + 2bd = 2xy</s>
</p>
<p style="it">
  <s xml:id="echoid-s3218" xml:space="preserve">et ac + bd = xy</s>
</p>
<p style="it">
  <s xml:id="echoid-s3219" xml:space="preserve">iterum ſubſtitutis aequipollentibus x et y <lb/>ac+bd=Va<emph style="super">2</emph>+b<emph style="super">2</emph>. </s>
  <s xml:id="echoid-s3220" xml:space="preserve">Vc<emph style="super">2</emph>+d<emph style="super">2</emph>.</s>
  <s xml:id="echoid-s3221" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3222" xml:space="preserve">facta irrationalium multiplicatione, (§ 30. </s>
  <s xml:id="echoid-s3223" xml:space="preserve">Anal. </s>
  <s xml:id="echoid-s3224" xml:space="preserve">finit.) <lb/></s>
  <s xml:id="echoid-s3225" xml:space="preserve">ac+bd=Vc<emph style="super">2</emph>a<emph style="super">2</emph>+c<emph style="super">2</emph>b<emph style="super">2</emph>+a<emph style="super">2</emph>d<emph style="super">2</emph>+b<emph style="super">2</emph>d<emph style="super">2</emph></s>
</p>
<p style="it">
  <s xml:id="echoid-s3226" xml:space="preserve">ut ſignum radicale tollatur, fiat quadratum ex ac + bd, et fiet <lb/>a<emph style="super">2</emph>c<emph style="super">2</emph> + 2acbd + b<emph style="super">2</emph>d<emph style="super">2</emph> = c<emph style="super">2</emph>a<emph style="super">2</emph> + c<emph style="super">2</emph>b<emph style="super">2</emph> + a<emph style="super">2</emph>d<emph style="super">2</emph> + b<emph style="super">2</emph>d<emph style="super">2</emph></s>
</p>
<p style="it">
  <s xml:id="echoid-s3227" xml:space="preserve">deletis acqualibus <lb/>2acbd = c<emph style="super">2</emph>b<emph style="super">2</emph> + a<emph style="super">2</emph>d<emph style="super">2</emph>,</s>
</p>
<p style="it">
  <s xml:id="echoid-s3228" xml:space="preserve">ſequeretur ergo ex bac bypotbeſi, duo haec facta ultima aequalia <lb/>eſſe, id quod promiſcue ſumtis perpendiculis et baſibus, fieri nequit. <lb/></s>
  <s xml:id="echoid-s3229" xml:space="preserve">Interim tamen ex theor. </s>
  <s xml:id="echoid-s3230" xml:space="preserve">pythagorae conſtat, omnino promiſcue ſumta <lb/>perpendicula et baſes, ſiquidem angulum rectum capiant, triangu-<lb/>lum rectangulum formare. </s>
  <s xml:id="echoid-s3231" xml:space="preserve">illuſtratio exemplo ſpeciali facta rem to-<lb/>tam clariorem reddet. </s>
  <s xml:id="echoid-s3232" xml:space="preserve">ſint perpendicula 8 et 14 baſes 10 et 18 <lb/>per theor. </s>
  <s xml:id="echoid-s3233" xml:space="preserve">pyth. </s>
  <s xml:id="echoid-s3234" xml:space="preserve">erit 8<emph style="super">2</emph> + 10<emph style="super">2</emph> = □ bypotenuſae = 164 <lb/>et 14<emph style="super">2</emph> + 18<emph style="super">2</emph> = □ hypot. </s>
  <s xml:id="echoid-s3235" xml:space="preserve">= s20</s>
</p>
<p style="it">
  <s xml:id="echoid-s3236" xml:space="preserve">ſed ſecundum ſuperiorem hypotheſin foret <lb/>(8+14)<emph style="super">2</emph> + (10+18)<emph style="super">2</emph> = 484 + 784 = 1268 = 684 <lb/>quod manifeſto ueritati repugnat.</s>
  <s xml:id="echoid-s3237" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3238" xml:space="preserve">Attamen datur caſus, quo regula Voigtelii bene ſeſe haber, nem-<lb/>pe, quando triangula rectangula aequales babent angulos, et ſunilia <lb/>ſunt, ut ualeat analogia, (§. </s>
  <s xml:id="echoid-s3239" xml:space="preserve">68. </s>
  <s xml:id="echoid-s3240" xml:space="preserve">Geom.) <lb/></s>
  <s xml:id="echoid-s3241" xml:space="preserve">a:</s>
  <s xml:id="echoid-s3242" xml:space="preserve">b = c:</s>
  <s xml:id="echoid-s3243" xml:space="preserve">d ubi {bc/a} = d</s>
</p>
<p style="it">
  <s xml:id="echoid-s3244" xml:space="preserve">ſiquidem ſubſtituto in aequatione <lb/>2abcd = c<emph style="super">2</emph>b<emph style="super">2</emph> + a<emph style="super">2</emph>d<emph style="super">2</emph></s>
</p>
<p style="it">
  <s xml:id="echoid-s3245" xml:space="preserve">ualore d et d<emph style="super">2</emph>, prodit <lb/>2abc.</s>
  <s xml:id="echoid-s3246" xml:space="preserve">{bc/a} = c<emph style="super">2</emph>b<emph style="super">2</emph> + a<emph style="super">2</emph>.</s>
  <s xml:id="echoid-s3247" xml:space="preserve">{b<emph style="super">2</emph>c<emph style="super">2</emph>/a<emph style="super">2</emph>}</s>
</p>
<p style="it">
  <s xml:id="echoid-s3248" xml:space="preserve">boc eſt <lb/>2b<emph style="super">2</emph>c<emph style="super">2</emph> = 2b<emph style="super">2</emph>c<emph style="super">2</emph></s>
</p>
<pb o="69" file="0185" n="190"/>
</div>
<div xml:id="echoid-div138" type="section" level="1" n="101">
<head xml:id="echoid-head120" xml:space="preserve"><emph style="bf">PROBLEMA XI.</emph></head>
<p style="it">
  <s xml:id="echoid-s3249" xml:space="preserve">75. </s>
  <s xml:id="echoid-s3250" xml:space="preserve">Lineam rectam borizontalem in campo ducere.</s>
  <s xml:id="echoid-s3251" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3252" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3253" xml:space="preserve">Caſus 1. </s>
  <s xml:id="echoid-s3254" xml:space="preserve">quando aequalis eſtterrae ſu-<lb/>perficies, ut liber per eam proſpectus pateat, quilibet in-<lb/>telligit, rectam lineam horizontalem, baculis poſitis, et <lb/>menſuratis, funiculo horizonti parallelo, eorum interuallis, <lb/>donec integram longitudinem lineae componant, definiri. <lb/></s>
  <s xml:id="echoid-s3255" xml:space="preserve">Praeterea, ſi ex tenſo inter baculos funiculo, uel ſi malis <lb/>ex goniodicte, ſuſpendatur compaſſus, hora quoque in <lb/>quam linea dirigenda eſt, reperietur.</s>
  <s xml:id="echoid-s3256" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3257" xml:space="preserve">Caſus 2. </s>
  <s xml:id="echoid-s3258" xml:space="preserve">quando inaequalis eſt terrae ſuperficies, ſed <lb/>tamen talis, quae non impedit progreſſum, per lineam re-<lb/>ctam: </s>
  <s xml:id="echoid-s3259" xml:space="preserve">tum qua area plana eſt, determinatio lineae fiat, eo <lb/>quem diximus, modo, aſt ubi intercedunt colles, montes-<lb/>que, tum in locum baſeos horizontalis hypotenuſa ſuccedit. <lb/></s>
  <s xml:id="echoid-s3260" xml:space="preserve">Sit 1) ſurſum in colle Dh determinanda linea horizontalis <lb/>
<anchor type="note" xlink:label="note-0185-01a" xlink:href="note-0185-01"/>
6 Uln. </s>
  <s xml:id="echoid-s3261" xml:space="preserve">in radice collis pone baculum, et ſuper eum fige <lb/>goniodictem, quaere primum compaſſo lineae directio-<lb/>nem, deinceps dirige inſtrumenti mobile crus uerſus ſum-<lb/>mum collis, et e regione colloca baculum AD, metire li-<lb/>neam AC, que ſit 10 Uln. </s>
  <s xml:id="echoid-s3262" xml:space="preserve">et ſuſpenſa libella inueni angu-<lb/>lum C, 10 gr. </s>
  <s xml:id="echoid-s3263" xml:space="preserve">deinde pro hoc angulo baſin BC. </s>
  <s xml:id="echoid-s3264" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s3265" xml:space="preserve">48) 9678, <lb/>et tandem pro baſi g C 6 Ulnar. </s>
  <s xml:id="echoid-s3266" xml:space="preserve">ob ſimilitudinem triangu-<lb/>lorum ABC, et eg C infer</s>
</p>
<div xml:id="echoid-div138" type="float" level="2" n="1">
<note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">Figur. 12. <lb/>Tab. 2.</note>
</div>
<p>
  <s xml:id="echoid-s3267" xml:space="preserve">BC \\ 9678:</s>
  <s xml:id="echoid-s3268" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3269" xml:space="preserve">AC \\ 10=</s>
</p>
<p>
  <s xml:id="echoid-s3270" xml:space="preserve">gC \\ 6:</s>
  <s xml:id="echoid-s3271" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3272" xml:space="preserve">eC.</s>
  <s xml:id="echoid-s3273" xml:space="preserve">\\ 6073</s>
</p>
<p>
  <s xml:id="echoid-s3274" xml:space="preserve">aſſume hanc lineam in hypot@nuſa e C et perpendiculo de-<lb/>miſſo ex e, baculum in i ſtatue, ita in accliui ſuperficie li-<lb/>nea horizontali gC reſpondens dabitur. </s>
  <s xml:id="echoid-s3275" xml:space="preserve">Similiter 2) fi de-<lb/>orſum, ex A uerfus C<unsure/> in decliui ſolo indicanda efſet linea <lb/>aliqua. </s>
  <s xml:id="echoid-s3276" xml:space="preserve">iterum quaere lineae horam, et hypotenuſae AC an-<lb/>gulum et longitudinem, et inueni Af hypotenuſae porti-<lb/>onem, baſis Bh portioni accommodatam. </s>
  <s xml:id="echoid-s3277" xml:space="preserve">ubi uero 3) pro-
<pb o="70" file="0186" n="191"/>
pter nimiam montis decliuitatem uel accliuitatem, non <lb/>licet aſſumere talem hypotenuſam, quae ad integram baſin <lb/>definiendam ſufficiat, oportet duabus pluribusue partibus <lb/>eam componere.</s>
  <s xml:id="echoid-s3278" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3279" xml:space="preserve">Caſus 3. </s>
  <s xml:id="echoid-s3280" xml:space="preserve">Quando uel ob collium praecipitia, uel pro-<lb/>pter alia obſtacula imperuia, recta procedere non permitti-<lb/>tur, fiat menſuratio linearum ac, cd, de, ef, per amba-<lb/>
<anchor type="note" xlink:label="note-0186-01a" xlink:href="note-0186-01"/>
ges poſitarum, et diligenter huius menſionis ſuperterraneae, <lb/>directiones, et anguli annotentur. </s>
  <s xml:id="echoid-s3281" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s3282" xml:space="preserve">69.) </s>
  <s xml:id="echoid-s3283" xml:space="preserve">deinde, ubi ſu-<lb/>ſpicio eſt, appropinquare has ambages ad lineam definien-<lb/>dam, figatur ultimus baculus, et ſuo loco relinquatur, hinc <lb/>tertio ichnographia huius menſionis deſcribatur, (§. </s>
  <s xml:id="echoid-s3284" xml:space="preserve">70.) </s>
  <s xml:id="echoid-s3285" xml:space="preserve">et <lb/>in principio ducatur ſecundum horam debitam linea recta <lb/>ab, tum appropinquatio, uel etiam concurſus linearum <lb/>per ambages ductarum habebitur. </s>
  <s xml:id="echoid-s3286" xml:space="preserve">et ſi tandem, recte ſe-<lb/>cundum plagas mundi poſita ichnographia, applices, ad <lb/>ultimum baculum f, inſtrumentum lineationis, poteris, <lb/>uel perpendiculi fr, uel obliquae lineae fb, quae usque ad <lb/>extremum rectae in ſolo indicandae pertingit, ſitum ob-<lb/>ſeruare, ipſam uero lineam, fr, fb, ſcala metiri. </s>
  <s xml:id="echoid-s3287" xml:space="preserve">Qua co-<lb/>gnita, applicato ad baculum localem f goniodicte, ex quo <lb/>compaſſus pendet, baculis ulterius conſtitutis, lineae fr, <lb/>uel fb longitudinem, et ita alterum lineae ab extremum, <lb/>terminabis.</s>
  <s xml:id="echoid-s3288" xml:space="preserve"/>
</p>
<div xml:id="echoid-div139" type="float" level="2" n="2">
<note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">Figur. 13. <lb/>Tab. 2.</note>
</div>
</div>
<div xml:id="echoid-div141" type="section" level="1" n="102">
<head xml:id="echoid-head121" xml:space="preserve"><emph style="bf">CONSECTARIVM.</emph></head>
<p>
  <s xml:id="echoid-s3289" xml:space="preserve">76. </s>
  <s xml:id="echoid-s3290" xml:space="preserve"><emph style="bf">E</emph>tſi forſan quaereretur non extremum lineae, ſed medi-<lb/>um aliquod in eadem @unctum, plane eodem artificio <lb/>idem manifeſtabis, ſi circa idem in menſione ſubſtiteris, et tan-<lb/>dem in ichnographia uerum poſitum indagaueris.</s>
  <s xml:id="echoid-s3291" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div142" type="section" level="1" n="103">
<head xml:id="echoid-head122" xml:space="preserve"><emph style="bf">PROBLEMA XII.</emph></head>
<p style="it">
  <s xml:id="echoid-s3292" xml:space="preserve">77. </s>
  <s xml:id="echoid-s3293" xml:space="preserve">Loca in ſuperficie terrae ſubterraneis reſpondentia inuenire.</s>
  <s xml:id="echoid-s3294" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3295" xml:space="preserve">Reſolutio prima. </s>
  <s xml:id="echoid-s3296" xml:space="preserve">Si a principio fodinae, v. </s>
  <s xml:id="echoid-s3297" xml:space="preserve">g. <lb/></s>
  <s xml:id="echoid-s3298" xml:space="preserve">puteo, capti, et in ichnographia deſcripti anguli directio-
<pb o="71" file="0187" n="192"/>
num, una cum lineis horizontalibus adiacentibus, eodem <lb/>ordine, quo ſemet in ſpecubus ſubterraneis exceperunt, <lb/>ſupra terram, beneficio goniodictici inſtrumenti, diſpo-<lb/>nantur, et baculi locales ſtatuantur, tandem quodlibet <lb/>punctum ſubter terram alii ſupra terram oppoſitum re-<lb/>peries. </s>
  <s xml:id="echoid-s3299" xml:space="preserve">Enim uero quia minimus error in angulis et late-<lb/>ribus commiſſus, per totam praxin diffunditur et augetur, <lb/>hac ſolutione infrequentius artifices utuntur.</s>
  <s xml:id="echoid-s3300" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3301" xml:space="preserve">Reſolutio ſecunda per lineam rectam. </s>
  <s xml:id="echoid-s3302" xml:space="preserve">nempe ducatur a <lb/>
<anchor type="note" xlink:label="note-0187-01a" xlink:href="note-0187-01"/>
principio menſionis ad punctum, quod ſubterraneo in <lb/>ichnographia competit, linea recta Hi, eademque ſcala <lb/>menſuretur, tum, recte prius in partes mundi conuerſa <lb/>ichnographia, imponatur lineae HI organum lineationis, <lb/>et hora in compaſſo obſeruetur, et ſecundum huius horae <lb/>ductum, baculis poſitis, determinetur lineae IH longi-<lb/>tudo, (§. </s>
  <s xml:id="echoid-s3303" xml:space="preserve">7) ita reperietur punctum I ſupra terram, quod <lb/>alteri eiusdem nominis infra terram, imminet. </s>
  <s xml:id="echoid-s3304" xml:space="preserve">Verum <lb/>etiam haec methodus, quando per inaequale ſolum et per <lb/>ambages proceditur, difficultates ſuas habet, et errori oc-<lb/>caſionem dare poteſt.</s>
  <s xml:id="echoid-s3305" xml:space="preserve"/>
</p>
<div xml:id="echoid-div142" type="float" level="2" n="1">
<note position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">Figur. 11. <lb/>Tab. 2.</note>
</div>
<p>
  <s xml:id="echoid-s3306" xml:space="preserve">Reſolutio tertia, funiculo indefinito. </s>
  <s xml:id="echoid-s3307" xml:space="preserve">(mit der verlohr-<lb/>nen Schnur)</s>
</p>
<p>
  <s xml:id="echoid-s3308" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3309" xml:space="preserve">Ponitur facta ſpecuum ichnographia, et quo-<lb/>niam ex eadem innoteſcit, circa quam regionem, et in <lb/>qua diſtantia, ſupra terram punctum dato infra terram in-<lb/>cumbens, haereat, ſume funiculum longum 6 uel 10 ulnas, <lb/>et progredere uerſus illud punctum in campo libero, et <lb/>utrimque in extremis funiculi pone baculos, (uel princi-<lb/>pio funiculum in machina tractoria putei alliga, et altero <lb/>tantum in fine palum ſtatue)</s>
</p>
<p>
  <s xml:id="echoid-s3310" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3311" xml:space="preserve">Deinde ex fune tenſo libellam, poſtea etiam com-<lb/>paſſum, ſuſpende, et ita angulum inclinationis et directio-<lb/>nis, cum longitudine funis, in pugillares refer.</s>
  <s xml:id="echoid-s3312" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3313" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3314" xml:space="preserve">Ita porro menſionem ſubdialem continua, donec
<pb o="72" file="0188" n="193"/>
ſuſpicio eſt, te prope punctum quaeſitum perueniſſe. </s>
  <s xml:id="echoid-s3315" xml:space="preserve">et il-<lb/>lo loco palum fige.</s>
  <s xml:id="echoid-s3316" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3317" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3318" xml:space="preserve">Domi fac ichnographiam menſionis ſubdialis, <lb/>(§. </s>
  <s xml:id="echoid-s3319" xml:space="preserve">70) ita quidem, uti ex eodem principio ducatur, tum <lb/>haec ipſa, tum antea quaeſita ueſtigii ſpecuum deſcriptio, <lb/>
<anchor type="note" xlink:label="note-0188-01a" xlink:href="note-0188-01"/>
quemadmodum in figura adiecta bcdnm ichnographia ſpe-<lb/>cuum, et axye ueſtigium menſionis ſubdialis eſt.</s>
  <s xml:id="echoid-s3320" xml:space="preserve"/>
</p>
<div xml:id="echoid-div143" type="float" level="2" n="2">
<note position="left" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">Figur. 10.</note>
</div>
<p>
  <s xml:id="echoid-s3321" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3322" xml:space="preserve">Sic enim manifeſtum fiet, quantum figurarum, iuxta <lb/>ſe poſitarum, fines e et m diſtent, et qualem ſitum mutu-<lb/>um habeant.</s>
  <s xml:id="echoid-s3323" xml:space="preserve">nempe applicatur ad e inſtrumentum lineatio-<lb/>nis, et hora lineae em notatur, ſcalaque eiusdem extenſio-<lb/>nis magnitudo menſuratur.</s>
  <s xml:id="echoid-s3324" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3325" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3326" xml:space="preserve">Hinc accede ad palum localem e, et ſecundum ho-<lb/>ram, quam compaſſus ſub goniodicte indicabit, lineam <lb/>cognitam em baculis determina, et ipſum punctum ſiue <lb/>locum m, palo itidem ſignandum, cognoſces.</s>
  <s xml:id="echoid-s3327" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div145" type="section" level="1" n="104">
<head xml:id="echoid-head123" xml:space="preserve"><emph style="bf">CONSECTARIVM I.</emph></head>
<p>
  <s xml:id="echoid-s3328" xml:space="preserve">78. </s>
  <s xml:id="echoid-s3329" xml:space="preserve"><emph style="bf">U</emph>ltima ſolutio prioribus abſque dubio praeſtat. </s>
  <s xml:id="echoid-s3330" xml:space="preserve">Siqui-<lb/>dem abſtinet a laboriofa incertaque uel lineae rectae <lb/>determinatione, uel imitatione multorum angulorum; </s>
  <s xml:id="echoid-s3331" xml:space="preserve">ſed id <lb/>unice agitur, ut menſionis ſubterraneae et ſuperterraneae <lb/>ichnographiae componantur. </s>
  <s xml:id="echoid-s3332" xml:space="preserve">Si igitur ſaltem debita diligen-<lb/>tia utramque quaeſieris, non eſt de accurata puncti optati defi-<lb/>nitione dubitandum. </s>
  <s xml:id="echoid-s3333" xml:space="preserve">Accedit his, quod, quia in inſtituenda <lb/>menſione ſubdiali, menſori liberum eſt, quam uelit in pro-<lb/>greſſu tenere uiam, poſſit euitare multa obſtacula, quae cum <lb/>taedio et erroris periculo ſuperanda erant, ſi uellet uel ſecun-<lb/>dum lineam rectam, uel per angulorum anfractus pergere.</s>
  <s xml:id="echoid-s3334" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div146" type="section" level="1" n="105">
<head xml:id="echoid-head124" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3335" xml:space="preserve">79. </s>
  <s xml:id="echoid-s3336" xml:space="preserve">Interim propoſita a <emph style="sc">Voigtelio</emph> p. </s>
  <s xml:id="echoid-s3337" xml:space="preserve">112. </s>
  <s xml:id="echoid-s3338" xml:space="preserve">monita hic notanda <lb/>ſunt. </s>
  <s xml:id="echoid-s3339" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3340" xml:space="preserve">ut eo loco, quo menſio facta eſt, etiam ichnographia ela-<lb/>boretur, ne in locis remotioribus, mutata magneticae acus declina-<lb/>tio, pragmatiam perturbet. </s>
  <s xml:id="echoid-s3341" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3342" xml:space="preserve">ut ſupra terram funes non nimis longi <lb/>adhibeantur, ſiquidem, cum leue uitium in angulis admittitur, illud <lb/>tanto plus nocet, tantoque magis augetur, quanto lineae exiſtunt <lb/>longiores.</s>
  <s xml:id="echoid-s3343" xml:space="preserve"/>
</p>
<pb o="73" file="0189" n="194"/>
</div>
<div xml:id="echoid-div147" type="section" level="1" n="106">
<head xml:id="echoid-head125" xml:space="preserve">CONSECTARIVM II.</head>
<p>
  <s xml:id="echoid-s3344" xml:space="preserve">80. </s>
  <s xml:id="echoid-s3345" xml:space="preserve"><emph style="bf">P</emph>orro ex dictis fluit praxis menſionis proprie ſic dictae, <lb/>(das Vermeſſen) quando a geometra ſpatium termina-<lb/>tur, intra quod demenſa (die Maaſſen) fodinarum, quorum <lb/>alicui uſusfructus a principe conceſſus eſt, continentur.</s>
  <s xml:id="echoid-s3346" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div148" type="section" level="1" n="107">
<head xml:id="echoid-head126" xml:space="preserve">CONSECTARIVM III.</head>
<p>
  <s xml:id="echoid-s3347" xml:space="preserve">81. </s>
  <s xml:id="echoid-s3348" xml:space="preserve"><emph style="bf">P</emph>raeterea apparet, cognito termino ſupra terram, poſſe <lb/>uiciſſim ei reſpondens punctum ſub terra in cryptis mon-<lb/>ſtrari, conuerſa ſuperioris probl. </s>
  <s xml:id="echoid-s3349" xml:space="preserve">praxi. </s>
  <s xml:id="echoid-s3350" xml:space="preserve">germ. </s>
  <s xml:id="echoid-s3351" xml:space="preserve">Lochſteine in die <lb/>grube faellen. </s>
  <s xml:id="echoid-s3352" xml:space="preserve">conf. </s>
  <s xml:id="echoid-s3353" xml:space="preserve">§. </s>
  <s xml:id="echoid-s3354" xml:space="preserve">14.</s>
  <s xml:id="echoid-s3355" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div149" type="section" level="1" n="108">
<head xml:id="echoid-head127" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3356" xml:space="preserve">82. </s>
  <s xml:id="echoid-s3357" xml:space="preserve"><emph style="bf">Q</emph>ualis autem quolibet loco menſurarum proportio in uſu ſit, <lb/>geometra a metallariis, uel iis, qui fodinis praefecti ſunt, <lb/>facile reſciſcet. </s>
  <s xml:id="echoid-s3358" xml:space="preserve">teſte Schoenbergio u. </s>
  <s xml:id="echoid-s3359" xml:space="preserve">Lehen p. </s>
  <s xml:id="echoid-s3360" xml:space="preserve">62, ſpatium quod <lb/>metalla indagaturis princeps, per magiſtrum metallicorum, tanquam <lb/>fendum uel emphyteuſin, ſub conditione decimarum praeſtandarum <lb/>concedit, habet 7 uln. </s>
  <s xml:id="echoid-s3361" xml:space="preserve">pro longitudine, et 7 uln. </s>
  <s xml:id="echoid-s3362" xml:space="preserve">pro latitudine uoca-<lb/>tur quadratum, (die Vierung) clauſum ſpatium uel clauſtrum <lb/>(Wehr) duo quadrata, fodina (fundgrube) tria clauſa ſpatia, <lb/>demenſum (Maas.) </s>
  <s xml:id="echoid-s3363" xml:space="preserve">duo clauſtra complectitur. </s>
  <s xml:id="echoid-s3364" xml:space="preserve">conſulatur etiam D. <lb/></s>
  <s xml:id="echoid-s3365" xml:space="preserve"><emph style="sc">Hertwig</emph> Berg-Buch. </s>
  <s xml:id="echoid-s3366" xml:space="preserve">u. </s>
  <s xml:id="echoid-s3367" xml:space="preserve">Lehn. </s>
  <s xml:id="echoid-s3368" xml:space="preserve">wehr. </s>
  <s xml:id="echoid-s3369" xml:space="preserve">maaſſen. </s>
  <s xml:id="echoid-s3370" xml:space="preserve">etc.</s>
  <s xml:id="echoid-s3371" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div150" type="section" level="1" n="109">
<head xml:id="echoid-head128" xml:space="preserve"><emph style="bf">PROBLEMA XIII.</emph></head>
<p style="it">
  <s xml:id="echoid-s3372" xml:space="preserve">83. </s>
  <s xml:id="echoid-s3373" xml:space="preserve"><emph style="bf">I</emph>nuenire lineam rectam, per quam ad cryptas breuiſſima uia <lb/>accedi poſſit. </s>
  <s xml:id="echoid-s3374" xml:space="preserve">(germ. </s>
  <s xml:id="echoid-s3375" xml:space="preserve">einen durchſchlag anzugeben) <lb/>Reſolutio. </s>
  <s xml:id="echoid-s3376" xml:space="preserve">Caſus 1. </s>
  <s xml:id="echoid-s3377" xml:space="preserve">Quando ex terrae ſuperficie eſt ad ſpe-<lb/>cum penetrandum.</s>
  <s xml:id="echoid-s3378" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3379" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3380" xml:space="preserve">Velim accedere ex B ad D, uel eo puteum agere. <lb/></s>
  <s xml:id="echoid-s3381" xml:space="preserve">
<anchor type="note" xlink:label="note-0189-01a" xlink:href="note-0189-01"/>
primo omnium, quaere ſu@ra terram punctum B, quod <lb/>imminet puncto D. </s>
  <s xml:id="echoid-s3382" xml:space="preserve">(§. </s>
  <s xml:id="echoid-s3383" xml:space="preserve">77)</s>
</p>
<div xml:id="echoid-div150" type="float" level="2" n="1">
<note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">Figur. 22.</note>
</div>
<p>
  <s xml:id="echoid-s3384" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3385" xml:space="preserve">Quaere ex caſu cryptarum et areae ſubdialis, per-<lb/>pendiculi B D longitudinem, (§. </s>
  <s xml:id="echoid-s3386" xml:space="preserve">73) et ſatis fiet petito.</s>
  <s xml:id="echoid-s3387" xml:space="preserve"/>
</p>
<p style="it">
  <s xml:id="echoid-s3388" xml:space="preserve">Caſus 2. </s>
  <s xml:id="echoid-s3389" xml:space="preserve">quando ex ſpecu ad uicinum cupis penetrare. </s>
  <s xml:id="echoid-s3390" xml:space="preserve">(g. </s>
  <s xml:id="echoid-s3391" xml:space="preserve">ein <lb/>querſchlag)</s>
</p>
<p>
  <s xml:id="echoid-s3392" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3393" xml:space="preserve">proponuntur copulanda puncta cryptarum G et F. <lb/></s>
  <s xml:id="echoid-s3394" xml:space="preserve">
<anchor type="note" xlink:label="note-0189-02a" xlink:href="note-0189-02"/>
fac initium menſionis a puncto alterutro v. </s>
  <s xml:id="echoid-s3395" xml:space="preserve">g F, et eam
<pb o="74" file="0190" n="195"/>
ſurſum per puteum ſupra terram, continua, usque ad pu-<lb/>teum, qui ad uicinam cauernam ducit, (§. </s>
  <s xml:id="echoid-s3396" xml:space="preserve">52. </s>
  <s xml:id="echoid-s3397" xml:space="preserve">69) ingredere <lb/>etiam puteum, donec ſuſpicari potes, ex captis numeris, <lb/>te ſimilem utrimque perpendicularem locorum profundi-<lb/>tatem obtinuiſſe;</s>
  <s xml:id="echoid-s3398" xml:space="preserve"/>
</p>
<div xml:id="echoid-div151" type="float" level="2" n="2">
<note position="right" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">Figur. 23</note>
</div>
<p>
  <s xml:id="echoid-s3399" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3400" xml:space="preserve">Fac ichnographias tuae menſionis, (§. </s>
  <s xml:id="echoid-s3401" xml:space="preserve">64. </s>
  <s xml:id="echoid-s3402" xml:space="preserve">71) con-<lb/>nexas, et ſi iam in deſiderata horizontali linea extrema <lb/>menſionis repereris, (nam ſi nondum id factum eſt, progre-<lb/>diendo uel regrediendo illum ſitum reperies) applica in-<lb/>ſtrumentum lineationis ad puncta G et F, et horam lineae <lb/>eo ducendae, et foſſoribus indicandae inuenies. </s>
  <s xml:id="echoid-s3403" xml:space="preserve">ſimile ex-<lb/>emplum eſt linea D F. </s>
  <s xml:id="echoid-s3404" xml:space="preserve">Fig. </s>
  <s xml:id="echoid-s3405" xml:space="preserve">II. </s>
  <s xml:id="echoid-s3406" xml:space="preserve">longa 9 {3/4} Uln. </s>
  <s xml:id="echoid-s3407" xml:space="preserve">et ducenda <lb/>ſub h 10, 4 {1/2}</s>
</p>
<p>
  <s xml:id="echoid-s3408" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3409" xml:space="preserve">Cum autem cryptarum copulandarum, v. </s>
  <s xml:id="echoid-s3410" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3411" xml:space="preserve">puncto-<lb/>rum HF diuerſae ſunt horizontales, quaerere oportet, <lb/>quanto F ſit altius, quam H, (§. </s>
  <s xml:id="echoid-s3412" xml:space="preserve">74) et quia in triangulo <lb/>GFH duo crura nota ſunt, inde hypotenuſa innoteſcet, <lb/>(§. </s>
  <s xml:id="echoid-s3413" xml:space="preserve">47) horam autem in ichnographia compaſſus manife-<lb/>ſtabit. </s>
  <s xml:id="echoid-s3414" xml:space="preserve">in fig. </s>
  <s xml:id="echoid-s3415" xml:space="preserve">11. </s>
  <s xml:id="echoid-s3416" xml:space="preserve">linea IL deſignat uiam ex cuniculo IM, ad <lb/>puteum A, quae 24 {1/4} Uln. </s>
  <s xml:id="echoid-s3417" xml:space="preserve">longa et in h. </s>
  <s xml:id="echoid-s3418" xml:space="preserve">7. </s>
  <s xml:id="echoid-s3419" xml:space="preserve">directa eſt.</s>
  <s xml:id="echoid-s3420" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div153" type="section" level="1" n="110">
<head xml:id="echoid-head129" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s3421" xml:space="preserve">84. </s>
  <s xml:id="echoid-s3422" xml:space="preserve"><emph style="bf">Q</emph>uanda ſurſum copulandae ſunt cryptae, v. </s>
  <s xml:id="echoid-s3423" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3424" xml:space="preserve">ad aquas ex ſupe-<lb/>riore in inferiorem cuniculum auertendas, cauto opus eſt, ue <lb/>foſſores, aqua attenuatum parietem perrumpente, mergantur. </s>
  <s xml:id="echoid-s3425" xml:space="preserve">quem <lb/>in finem eum aliquo usque perrectum fuit, praelonga terebra modi-<lb/>cum aperitur foramen, ut aqua ſenſim prius abducatur. </s>
  <s xml:id="echoid-s3426" xml:space="preserve">v. </s>
  <s xml:id="echoid-s3427" xml:space="preserve">V<emph style="sc">OIG-<lb/>TEL.</emph> p. </s>
  <s xml:id="echoid-s3428" xml:space="preserve">139.</s>
  <s xml:id="echoid-s3429" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div154" type="section" level="1" n="111">
<head xml:id="echoid-head130" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s3430" xml:space="preserve">85 <emph style="bf">S</emph>atis actum eſt de cryptis ducendis et metiendis. </s>
  <s xml:id="echoid-s3431" xml:space="preserve">ſequitur caput <lb/>de uenis metallicis, earumque iudicio et menſione. </s>
  <s xml:id="echoid-s3432" xml:space="preserve">quod qui-<lb/>dem implicatias eſt, quia hic ſubinde fallunt ſpem noſtram, dubii de-<lb/>liteſcentium in terrae uiſceribus metallorum indices, dum nimirum <lb/>meliores ignor antur. </s>
  <s xml:id="echoid-s3433" xml:space="preserve">optarem, ut hoc caput, ſpeciatim, quoad uena-<lb/>rum diiudicationem, uberius excultum, et plenius, a uiro experientia <lb/>talium rerum ſatis inſtructo, elaboratum eſſet, quippe quod ad feli-
<pb o="75" file="0191" n="196"/>
cem metallorum indagationem uel maxime conducit; </s>
  <s xml:id="echoid-s3434" xml:space="preserve">uerum, cum <lb/>hactenus non niſi ſparſim aliquas de eo obſeruationes ſcriptores habe-<lb/>ant, ego uero de propriis experimentis gloriari nequeam, mihi id <lb/>duntaxat efficiendum intelligo, ut ex iis, quae alii metallorum pe-<lb/>riti tradiderunt, ſeligam inprimis ea, in quibus geometriae uſus <lb/>cernitur, et quae ad uenas iam detectas ſpectant. </s>
  <s xml:id="echoid-s3435" xml:space="preserve">Interea etiam hic <lb/>breuis ero, quia difficile eſt, de uenis agere, niſi quis in rem prae-<lb/>ſentem ducatur. </s>
  <s xml:id="echoid-s3436" xml:space="preserve">conf. </s>
  <s xml:id="echoid-s3437" xml:space="preserve"><emph style="sc">Agricolae</emph> Bermannus. </s>
  <s xml:id="echoid-s3438" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3439" xml:space="preserve">449. </s>
  <s xml:id="echoid-s3440" xml:space="preserve">ſq. <lb/></s>
  <s xml:id="echoid-s3441" xml:space="preserve"><emph style="sc">Löhneyss</emph> d. </s>
  <s xml:id="echoid-s3442" xml:space="preserve">metallis. </s>
  <s xml:id="echoid-s3443" xml:space="preserve">Part. </s>
  <s xml:id="echoid-s3444" xml:space="preserve">I. </s>
  <s xml:id="echoid-s3445" xml:space="preserve">f. </s>
  <s xml:id="echoid-s3446" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3447" xml:space="preserve">ſq.</s>
  <s xml:id="echoid-s3448" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div155" type="section" level="1" n="112">
<head xml:id="echoid-head131" xml:space="preserve"><emph style="bf">DEFINITIO XX.</emph></head>
<p>
  <s xml:id="echoid-s3449" xml:space="preserve">86. </s>
  <s xml:id="echoid-s3450" xml:space="preserve"><emph style="bf">V</emph>ena metallica (ein Gang) quam foſſores ſpecubus ſuis <lb/>perſequuntur, eſt in longum per terram porrecta me-<lb/>talli materies, quae a reptatu, quo uenarum ſanguinis ani-<lb/>mantium ſimilitudinem refert, illud nomen accepit. </s>
  <s xml:id="echoid-s3451" xml:space="preserve">quae-<lb/>libet uena foſſoribus dicitur habere pendentem et iacen-<lb/>tem partem; </s>
  <s xml:id="echoid-s3452" xml:space="preserve">(das hangende und liegende) pendens eſt, <lb/>quae uelut tegumentum uenae ſurſum incumbit, iacens, <lb/>in quam uena recumbit.</s>
  <s xml:id="echoid-s3453" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div156" type="section" level="1" n="113">
<head xml:id="echoid-head132" xml:space="preserve"><emph style="bf">DEFINITIO XXI.</emph></head>
<p>
  <s xml:id="echoid-s3454" xml:space="preserve">87. </s>
  <s xml:id="echoid-s3455" xml:space="preserve"><emph style="bf">F</emph>ibrae (Klüfte) ſunt uenulae, ex trunco ampliore dif-<lb/>fuſae, transuerſae, obliquae, uenae modo coniunctae <lb/>modo eidem incumbentes.</s>
  <s xml:id="echoid-s3456" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div157" type="section" level="1" n="114">
<head xml:id="echoid-head133" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s3457" xml:space="preserve">88. </s>
  <s xml:id="echoid-s3458" xml:space="preserve"><emph style="bf">D</emph>e notis uenarum <emph style="sc">Agricola</emph> 1. </s>
  <s xml:id="echoid-s3459" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3460" xml:space="preserve">ſcribit: </s>
  <s xml:id="echoid-s3461" xml:space="preserve">uenarum omni-<lb/>um, quantum in extenſione longe eſt optima, quae ab oriente <lb/>in occidentem extenditur per montis decliue, ita tamen, ut dorſum <lb/>montis uerſus meridiem ſit, decliue uero ipſius in ſeptentrionem ſen-<lb/>ſim inclinet. </s>
  <s xml:id="echoid-s3462" xml:space="preserve">proxima uero bon@@ate eſt, quae a media aliqua orientis <lb/>et meridiei parte, in mediam rurſus occidentis et ſeptentrionis ex-<lb/>tenditur, atque eiusmodi eſt uena, quam ſtellam uocari dixi. </s>
  <s xml:id="echoid-s3463" xml:space="preserve">reli-<lb/>quae aut quanto plus a dictis illis receſſerint, tanto minus argenti <lb/>feraces eſſe ſolent. </s>
  <s xml:id="echoid-s3464" xml:space="preserve">add. </s>
  <s xml:id="echoid-s3465" xml:space="preserve">L<emph style="sc">ÖHNEYSS.</emph> l. </s>
  <s xml:id="echoid-s3466" xml:space="preserve">c.</s>
  <s xml:id="echoid-s3467" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div158" type="section" level="1" n="115">
<head xml:id="echoid-head134" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s3468" xml:space="preserve">89. </s>
  <s xml:id="echoid-s3469" xml:space="preserve"><emph style="bf">V</emph>enae nondum detectae uel earum progreſſus ac continuationes <lb/>uirgula diuinatoria quaeruntur, quam nonnunquam geometra
<pb o="76" file="0192" n="197"/>
etiam ſequatur oportet. </s>
  <s xml:id="echoid-s3470" xml:space="preserve">Huius inſtrumenti effectus mirabiles data <lb/>opera explicare nititur L. </s>
  <s xml:id="echoid-s3471" xml:space="preserve">L. </s>
  <s xml:id="echoid-s3472" xml:space="preserve">de <emph style="sc">Vallemont</emph> Th. </s>
  <s xml:id="echoid-s3473" xml:space="preserve">D. </s>
  <s xml:id="echoid-s3474" xml:space="preserve">in tr. </s>
  <s xml:id="echoid-s3475" xml:space="preserve">cui <lb/>titulus, la phyſique occulte, ou traité de la baguette diuina-<lb/>toire, et de ſon utilite, pour la decouverte des ſources d' eau, <lb/>des minieres, des treſors cachez, des voleurs et des meurtriers <lb/>fugitifs. </s>
  <s xml:id="echoid-s3476" xml:space="preserve">ed. </s>
  <s xml:id="echoid-s3477" xml:space="preserve">Pariſ. </s>
  <s xml:id="echoid-s3478" xml:space="preserve">1709. </s>
  <s xml:id="echoid-s3479" xml:space="preserve">12. </s>
  <s xml:id="echoid-s3480" xml:space="preserve">hoc enim libro cupit demonſtrare auctor, <lb/>uirgulae motum oriri, ab exhalationibus, aquarum, uenarum metal-<lb/>licarum, item corporum defunctorum, uel etiam corporis furis aut <lb/>homicidae fugitiui, ſumma animi anxietate laborantis, et ob per-<lb/>petuos terrores, et praecipitem fugam, copioſiares ſolito uapores ex-<lb/>ſpirantis, u. </s>
  <s xml:id="echoid-s3481" xml:space="preserve">c. </s>
  <s xml:id="echoid-s3482" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3483" xml:space="preserve">7. </s>
  <s xml:id="echoid-s3484" xml:space="preserve">8. </s>
  <s xml:id="echoid-s3485" xml:space="preserve">add. </s>
  <s xml:id="echoid-s3486" xml:space="preserve"><emph style="sc">Athan</emph>. </s>
  <s xml:id="echoid-s3487" xml:space="preserve"><emph style="sc">Kircheri</emph> ars magnetica <lb/>l. </s>
  <s xml:id="echoid-s3488" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3489" xml:space="preserve">P. </s>
  <s xml:id="echoid-s3490" xml:space="preserve">s.</s>
  <s xml:id="echoid-s3491" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3492" xml:space="preserve">634. </s>
  <s xml:id="echoid-s3493" xml:space="preserve"><emph style="sc">Act</emph>. </s>
  <s xml:id="echoid-s3494" xml:space="preserve"><emph style="sc">Philos</emph>. </s>
  <s xml:id="echoid-s3495" xml:space="preserve">ſociet. </s>
  <s xml:id="echoid-s3496" xml:space="preserve">angl. </s>
  <s xml:id="echoid-s3497" xml:space="preserve">Oldenburgii. </s>
  <s xml:id="echoid-s3498" xml:space="preserve">a. </s>
  <s xml:id="echoid-s3499" xml:space="preserve">1668. <lb/></s>
  <s xml:id="echoid-s3500" xml:space="preserve">m. </s>
  <s xml:id="echoid-s3501" xml:space="preserve">ſept. </s>
  <s xml:id="echoid-s3502" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3503" xml:space="preserve">642. </s>
  <s xml:id="echoid-s3504" xml:space="preserve"><emph style="sc">Casp</emph>. </s>
  <s xml:id="echoid-s3505" xml:space="preserve"><emph style="sc">Schotti</emph> magia uniuerſalis naturae et <lb/>artis. </s>
  <s xml:id="echoid-s3506" xml:space="preserve">P. </s>
  <s xml:id="echoid-s3507" xml:space="preserve">IV. </s>
  <s xml:id="echoid-s3508" xml:space="preserve">lib. </s>
  <s xml:id="echoid-s3509" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3510" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3511" xml:space="preserve">420. </s>
  <s xml:id="echoid-s3512" xml:space="preserve">ſq. </s>
  <s xml:id="echoid-s3513" xml:space="preserve">ubi etiam p. </s>
  <s xml:id="echoid-s3514" xml:space="preserve">426, grauem uirgulae cen-<lb/>ſuram ab Agricola ſcriptam inſeruit. </s>
  <s xml:id="echoid-s3515" xml:space="preserve">Olim uirgulae uſus ſuperſtitio-<lb/>ne non carebat. </s>
  <s xml:id="echoid-s3516" xml:space="preserve">uerum hodie conſtat inter metallarios, electionem <lb/>putationemue uirgae arbitrariam eſſe, et quolibet tempore et loco <lb/>ramulum bifidum corylaceum ſalignumque aſſumi poſſe, quin uidi <lb/>Freibergae foſſorem, qui uirga, ex filo cupreo craſſiore contorto, facta, <lb/>ad ſpecus aquaſque inueſtigandas utebatur. </s>
  <s xml:id="echoid-s3517" xml:space="preserve">Interim etiam id certum <lb/>eſt, nec omnium in hominum manibus tremere uirgulam, nec ſemper <lb/>uenas absque errore indicare.</s>
  <s xml:id="echoid-s3518" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div159" type="section" level="1" n="116">
<head xml:id="echoid-head135" xml:space="preserve">SCHOLION III.</head>
<p style="it">
  <s xml:id="echoid-s3519" xml:space="preserve">90. </s>
  <s xml:id="echoid-s3520" xml:space="preserve"><emph style="bf">D</emph>n. </s>
  <s xml:id="echoid-s3521" xml:space="preserve">I. </s>
  <s xml:id="echoid-s3522" xml:space="preserve">G. </s>
  <s xml:id="echoid-s3523" xml:space="preserve"><emph style="sc">Hübschivs</emph> mathematicus ſcholae illuſtris por-<lb/>tenſis clariſſimus, miſit nuper ad me aliquot paginas manu-<lb/>ſcriptas incerti auctoris, in quibus enixe commendatur, pro uenis <lb/>reperiundis, index peculiari artificio paratus. </s>
  <s xml:id="echoid-s3524" xml:space="preserve">nempe uult auctor, ut <lb/>oleum arte chimica metallorum ☉(sun), ☽, etc. </s>
  <s xml:id="echoid-s3525" xml:space="preserve">ueluti ſpiritu uel natiuis <lb/>halitibus imbuatur, deinde acus ferreae plures elaborentur, et ſingu-<lb/>lae duodecies ignitue et candentes in oleo, quod metalli, cui index <lb/>aptandus eſt, particulis abundat, toties reſtinguantur, atque ita me-<lb/>talli quaerendi elementis inficiantur. </s>
  <s xml:id="echoid-s3526" xml:space="preserve">tum iubet hunc indicem, in <lb/>mediam inter meridiem et ortum plagam conuerſum, in crypta, ubi <lb/>uena metallica aperitur, reponi, et expectari per horam dimidiam, <lb/>donec idem directus a proximi metalli halitibus ſubſiſtat. </s>
  <s xml:id="echoid-s3527" xml:space="preserve">ita enim <lb/>putat futurum, ut et quale metallum ſperandum ſit, et quorſum eius <lb/>uena tendat, cognoſcatur. </s>
  <s xml:id="echoid-s3528" xml:space="preserve">nam quando iners in priore ſitu manet in-<lb/>dex, colligit inde inuentor, metallum, cuius elementis ac uirtute
<pb o="77" file="0193" n="198"/>
gnomon imbutus fuit, ibi non reperiri. </s>
  <s xml:id="echoid-s3529" xml:space="preserve">aliumque ideo indicem cupit <lb/>applicari. </s>
  <s xml:id="echoid-s3530" xml:space="preserve">ſed haec peritioribus iudicanda relinquo.</s>
  <s xml:id="echoid-s3531" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div160" type="section" level="1" n="117">
<head xml:id="echoid-head136" xml:space="preserve"><emph style="bf">DEFINITIO XXII.</emph></head>
<p>
  <s xml:id="echoid-s3532" xml:space="preserve">91. </s>
  <s xml:id="echoid-s3533" xml:space="preserve"><emph style="bf">V</emph>enae tum conuerſione in mundi plagas, tum aſcenſu <lb/>lapſuque differunt. </s>
  <s xml:id="echoid-s3534" xml:space="preserve">prior poſitio parit diuiſionem fe-<lb/>quentem. </s>
  <s xml:id="echoid-s3535" xml:space="preserve">uena recta eſt, (ſtehender gang), cuius linea dire-<lb/>ctionis (ſtreichen) cadit intra horas 12 et 3. </s>
  <s xml:id="echoid-s3536" xml:space="preserve">uena porrecta <lb/>(flacher gang) quae dirigitur intra horas 9-12. </s>
  <s xml:id="echoid-s3537" xml:space="preserve">uena ſerotina <lb/>(ſpatgang) quae uertitur intra arcum horarum 6-9. </s>
  <s xml:id="echoid-s3538" xml:space="preserve">uena <lb/>matutina, (morgengang) quae intra horas 3-6 continetur.</s>
  <s xml:id="echoid-s3539" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div161" type="section" level="1" n="118">
<head xml:id="echoid-head137" xml:space="preserve"><emph style="bf">DEFINITIO XXIII.</emph></head>
<p>
  <s xml:id="echoid-s3540" xml:space="preserve">92. </s>
  <s xml:id="echoid-s3541" xml:space="preserve"><emph style="bf">P</emph>ro aſcenſu uero et lapſu uenarum haec diuiſio placuit. <lb/></s>
  <s xml:id="echoid-s3542" xml:space="preserve">uena erecta, (ſtehender gang) cuius inclinatio ad ho-<lb/>rizontalem non eſt infra 80 gr. </s>
  <s xml:id="echoid-s3543" xml:space="preserve">quae nempe aut perpendi-<lb/>cularis eſt, aut a perpendiculo non ultra 10 gr. </s>
  <s xml:id="echoid-s3544" xml:space="preserve">deflectit. </s>
  <s xml:id="echoid-s3545" xml:space="preserve"><lb/>uena obliqua, (donlegter gang) cuius inclinatio ad horizon-<lb/>tem eſt infra 80 et 60 gr. </s>
  <s xml:id="echoid-s3546" xml:space="preserve">uena aequa, (flacher gang) cuius <lb/>inclinatio ad horizontalem eſt intra 50 et 20. </s>
  <s xml:id="echoid-s3547" xml:space="preserve">gr. </s>
  <s xml:id="echoid-s3548" xml:space="preserve">Ubi uero <lb/>inclinatio uenarum eſt infra 20 gr. </s>
  <s xml:id="echoid-s3549" xml:space="preserve">pendentes uel dilatatae <lb/>(ſchwebende gaenge) nuncupantur. </s>
  <s xml:id="echoid-s3550" xml:space="preserve">germ. </s>
  <s xml:id="echoid-s3551" xml:space="preserve">nonnunquam <lb/>etiam floeze dicuntur.</s>
  <s xml:id="echoid-s3552" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div162" type="section" level="1" n="119">
<head xml:id="echoid-head138" xml:space="preserve"><emph style="bf">DEFINITIO XXIV.</emph></head>
<p>
  <s xml:id="echoid-s3553" xml:space="preserve">93. </s>
  <s xml:id="echoid-s3554" xml:space="preserve"><emph style="bf">Q</emph>uando uenae conuerſionem ad mundi partes ſaepius <lb/>mutant, directio principalis (hauptſtreichen) appella-<lb/>tur, quae plerisque communis eſt.</s>
  <s xml:id="echoid-s3555" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div163" type="section" level="1" n="120">
<head xml:id="echoid-head139" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s3556" xml:space="preserve">94. </s>
  <s xml:id="echoid-s3557" xml:space="preserve"><emph style="bf">E</emph>rgo principalis directio, paralleliſmo plurium uenarum, <lb/>in eandem mundi partem tendentium, obtinetur.</s>
  <s xml:id="echoid-s3558" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div164" type="section" level="1" n="121">
<head xml:id="echoid-head140" xml:space="preserve">SCHOLION.</head>
<p style="it">
  <s xml:id="echoid-s3559" xml:space="preserve">95. </s>
  <s xml:id="echoid-s3560" xml:space="preserve"><emph style="bf">V</emph>enae, quae lapſu ſuo ſitum continue mutant, et modo erectae <lb/>modo<unsure/> obliquae, item in contrarias partes reflexae ſunt, prae-<lb/>cipitatae dicuntur. </s>
  <s xml:id="echoid-s3561" xml:space="preserve">(Sie ſtürzen ſich und fallen wiederſinns) et ta-<lb/>les non tam ab aſcenſu deſcenſuue, quam a conuerſione in mundi par-
<pb o="78" file="0194" n="199" rhead="GEOMETRIA SVBTERRANEA."/>
tes nominari et diſtingui merentur. </s>
  <s xml:id="echoid-s3562" xml:space="preserve">tales ſunt a, b, c, <unsure/> in fig. </s>
  <s xml:id="echoid-s3563" xml:space="preserve">24. </s>
  <s xml:id="echoid-s3564" xml:space="preserve">uid. <lb/></s>
  <s xml:id="echoid-s3565" xml:space="preserve"><emph style="sc">Voigtel</emph>. </s>
  <s xml:id="echoid-s3566" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3567" xml:space="preserve">120.</s>
  <s xml:id="echoid-s3568" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div165" type="section" level="1" n="122">
<head xml:id="echoid-head141" xml:space="preserve">PROBLEMA XIV.</head>
<p>
  <s xml:id="echoid-s3569" xml:space="preserve">96. </s>
  <s xml:id="echoid-s3570" xml:space="preserve">Venarun ſitum inueſtigare.</s>
  <s xml:id="echoid-s3571" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3572" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3573" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3574" xml:space="preserve">Quando intra cryptas, quae uenas <lb/>interſecant, hae iam manifeſtae ſunt, applicatur utrique <lb/>extremo, in iacente et pendente cauernae pariete, funicu-<lb/>lus, et ſuſpenſa libella et compaſſo, tum inclinatio tum di-<lb/>rectio quaeritur.</s>
  <s xml:id="echoid-s3575" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3576" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3577" xml:space="preserve">Hinc inueſtigata baſi, pro angulo dato, etiam in <lb/>ichnographia fodinae, loco ſibi competente, linea quae ſi-<lb/>tum uenae ob oculos ponat, ducitur. </s>
  <s xml:id="echoid-s3578" xml:space="preserve">tales f. </s>
  <s xml:id="echoid-s3579" xml:space="preserve">20. </s>
  <s xml:id="echoid-s3580" xml:space="preserve">occurrunt, <lb/>quarum ſitum etiam in menſione cryptarum <unsure/>notaui. </s>
  <s xml:id="echoid-s3581" xml:space="preserve">§. </s>
  <s xml:id="echoid-s3582" xml:space="preserve">59.</s>
  <s xml:id="echoid-s3583" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3584" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3585" xml:space="preserve">Qualis autem uerſus ſuperiorem terrae cruſtam ſit <lb/>poſitio uenarum, foſſor, qui uirgulam diuinatoriam rege-<lb/>re didicit, progreſſu ſuo indicabit, quem geometra metie-<lb/>tur, et figura etiam ob oculos ponet.</s>
  <s xml:id="echoid-s3586" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div166" type="section" level="1" n="123">
<head xml:id="echoid-head142" xml:space="preserve">CONSECTARIVM.</head>
<p>
  <s xml:id="echoid-s3587" xml:space="preserve">97. </s>
  <s xml:id="echoid-s3588" xml:space="preserve">Quando duarum uenarum ſitus intra terram et extra ter-<lb/>ram ſic innotuit, inde ſuſpicio ducitur, utrum ſe ſint ſe-<lb/>caturae, ſi continuentur. </s>
  <s xml:id="echoid-s3589" xml:space="preserve">nempe uenae, quarum diſtantia in-<lb/>fra minor, ſupra maior deprehenditur, quia conuergunt, ſe <lb/>tandem ſecabunt. </s>
  <s xml:id="echoid-s3590" xml:space="preserve">ſecus foret, ſi contraria earundem poſitio <lb/>eſiet.</s>
  <s xml:id="echoid-s3591" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div167" type="section" level="1" n="124">
<head xml:id="echoid-head143" xml:space="preserve">PROBLEMA XV.</head>
<p>
  <s xml:id="echoid-s3592" xml:space="preserve">98. </s>
  <s xml:id="echoid-s3593" xml:space="preserve">Inuenire directionem principalem uenarum.</s>
  <s xml:id="echoid-s3594" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3595" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3596" xml:space="preserve">I. </s>
  <s xml:id="echoid-s3597" xml:space="preserve">Ubi ia@ aperiere uenam, et ſecun-<lb/>dum eam ſpecus cauarunt foſſores, fiat eorum menſio, et <lb/>ichnographia, et ſiquidem, prope eandem horizontalem <lb/>lineam producantur, quaeratur directio principalis, ex plu-<lb/>rium baſium paralleliſmo.</s>
  <s xml:id="echoid-s3598" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3599" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3600" xml:space="preserve">Venae latentis adhuc directionem, uirgulae motus, <lb/>et uia foſſoris eam geſtantis, patefacient.</s>
  <s xml:id="echoid-s3601" xml:space="preserve"/>
</p>
<pb o="79" file="0195" n="200" rhead="GEOMETRIA SVBTERANEA."/>
</div>
<div xml:id="echoid-div168" type="section" level="1" n="125">
<head xml:id="echoid-head144" xml:space="preserve">SCHOLION I.</head>
<p>
  <s xml:id="echoid-s3602" xml:space="preserve">99. </s>
  <s xml:id="echoid-s3603" xml:space="preserve">Reliqua et intricatiora de uenis capita, ut obliquitas earum, <lb/>acceſſus ad easdem, et ſimilia curioſus talium ſcrutator re-<lb/>rum, non tam figuris, quam deſcenſu in fodinas, et uenarum, uariis <lb/>reptatibus inſignium, contemplatione, melius pleniusque intelliget. <lb/></s>
  <s xml:id="echoid-s3604" xml:space="preserve">Itaque cum etiam ad banc materiam ulterius colendam aditus a no-<lb/>bis paratus ſit, ulteriorem buius argumenti explicationem, nec non <lb/>de aquis ducendis doctrinam, cuius fundamenta ſolide in bydrauli-<lb/>cae inſtitutionibus tradita ſunt, mittam, et ad deſcriptiones fodina-<lb/>rum illuſtrandas progrediar.</s>
  <s xml:id="echoid-s3605" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div169" type="section" level="1" n="126">
<head xml:id="echoid-head145" xml:space="preserve">SCHOLION II.</head>
<p>
  <s xml:id="echoid-s3606" xml:space="preserve">100. </s>
  <s xml:id="echoid-s3607" xml:space="preserve">Enimuero, cum de ichnographia menſionis ſubterraneae et <lb/>ſubdialis copioſe ſupra §. </s>
  <s xml:id="echoid-s3608" xml:space="preserve">64. </s>
  <s xml:id="echoid-s3609" xml:space="preserve">67. </s>
  <s xml:id="echoid-s3610" xml:space="preserve">70. </s>
  <s xml:id="echoid-s3611" xml:space="preserve">dictum ſit, ſupereſt, ut <lb/>de orthographia et ſcenographia agatur.</s>
  <s xml:id="echoid-s3612" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div170" type="section" level="1" n="127">
<head xml:id="echoid-head146" xml:space="preserve">DEFINITIO XXV.</head>
<p>
  <s xml:id="echoid-s3613" xml:space="preserve">101. </s>
  <s xml:id="echoid-s3614" xml:space="preserve">Oribographia, ſiue profilum, uocatur delineatio, qua <lb/>mons, in quo fodinae actae ſunt, quaſi per medi-<lb/>am earum cauitatem ſectus ſiſtitur, ut ſuperiorum et infe-<lb/>riorum cryptarum poſitio, quoad perpendicularem altitu-<lb/>dinem, ob oculos ponatur.</s>
  <s xml:id="echoid-s3615" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div171" type="section" level="1" n="128">
<head xml:id="echoid-head147" xml:space="preserve">PROBLEMA XVI.</head>
<p>
  <s xml:id="echoid-s3616" xml:space="preserve">102. </s>
  <s xml:id="echoid-s3617" xml:space="preserve">Orthographiam fodinarum deſcribere.</s>
  <s xml:id="echoid-s3618" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3619" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3620" xml:space="preserve">Ducatur linea horizontalis OM, et ſuper <lb/>
<anchor type="note" xlink:label="note-0195-01a" xlink:href="note-0195-01"/>
ea erigantur locis competentibus perpendicula OA, QH, <lb/>quibus puteorum altitudines normales AN, QH ſcalae <lb/>adminiculo exhibentur, et praeterea parallelis ductibus eo-<lb/>rum amplitudines ſignificentur.</s>
  <s xml:id="echoid-s3621" xml:space="preserve"/>
</p>
<div xml:id="echoid-div171" type="float" level="2" n="1">
<note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">Figur. 11. <lb/>Tab. 2.</note>
</div>
<p>
  <s xml:id="echoid-s3622" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3623" xml:space="preserve">Quando deorſum a cryptis uel cuniculis alii putei <lb/>(geſenke) acti funt, etiam ulterius eorum altitudines pin-<lb/>gantur. </s>
  <s xml:id="echoid-s3624" xml:space="preserve">Et profilum fodinarum erit deſcriptum.</s>
  <s xml:id="echoid-s3625" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div173" type="section" level="1" n="129">
<head xml:id="echoid-head148" xml:space="preserve">DEFINITIO XXVI.</head>
<p>
  <s xml:id="echoid-s3626" xml:space="preserve">103. </s>
  <s xml:id="echoid-s3627" xml:space="preserve">Scenographia fodinarum menſoribus nominatur deli-<lb/>neatio, quae orthographiam iuxta ichnographiam <lb/>iunctim refert.</s>
  <s xml:id="echoid-s3628" xml:space="preserve"/>
</p>
<pb o="80" file="0196" n="201" rhead="GEOMETRIA SVBTERRANEA."/>
</div>
<div xml:id="echoid-div174" type="section" level="1" n="130">
<head xml:id="echoid-head149" xml:space="preserve">SCHOLION.</head>
<p>
  <s xml:id="echoid-s3629" xml:space="preserve">104. </s>
  <s xml:id="echoid-s3630" xml:space="preserve">Alias, apud ſcriptores opticos, ſcenographia, integri corporis et laterum <lb/>eiusdem recedentium, ſeque contrabentium, picturam ſignificat. </s>
  <s xml:id="echoid-s3631" xml:space="preserve">uerum <lb/>accipienda bic ſunt uocabula, prouti menſoribus ſunt uſitata.</s>
  <s xml:id="echoid-s3632" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div175" type="section" level="1" n="131">
<head xml:id="echoid-head150" xml:space="preserve">PROBLEMA XVII.</head>
<p>
  <s xml:id="echoid-s3633" xml:space="preserve">105. </s>
  <s xml:id="echoid-s3634" xml:space="preserve">Scenographiam fodinarum delineare.</s>
  <s xml:id="echoid-s3635" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s3636" xml:space="preserve">Reſolutio. </s>
  <s xml:id="echoid-s3637" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3638" xml:space="preserve">Deſcribatur ſecundum leges ſupra tra-<lb/>
<anchor type="note" xlink:label="note-0196-01a" xlink:href="note-0196-01"/>
ditas ichnographia. </s>
  <s xml:id="echoid-s3639" xml:space="preserve">IAKM.</s>
  <s xml:id="echoid-s3640" xml:space="preserve"/>
</p>
<div xml:id="echoid-div175" type="float" level="2" n="1">
<note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">Figur. 11. <lb/>Tab. 2.</note>
</div>
<p>
  <s xml:id="echoid-s3641" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3642" xml:space="preserve">Eidem ſubiiciatur orthographia AOM, et demittantur <lb/>a puteis A, H, item loco terminato i, nec non cuniculi oſtio <lb/>M, rectae perpendiculares, ad horizontalem, quibus coniun-<lb/>ctio partium illarum ob oculos ponatur, et habebitur ſceno-<lb/>graphia.</s>
  <s xml:id="echoid-s3643" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div177" type="section" level="1" n="132">
<head xml:id="echoid-head151" xml:space="preserve">SCHOLION I.</head>
<p style="it">
  <s xml:id="echoid-s3644" xml:space="preserve">106. </s>
  <s xml:id="echoid-s3645" xml:space="preserve">VOIGTEL. </s>
  <s xml:id="echoid-s3646" xml:space="preserve">p. </s>
  <s xml:id="echoid-s3647" xml:space="preserve">191. </s>
  <s xml:id="echoid-s3648" xml:space="preserve">deſiderat etiam menſionis ſubdialis icbnograpbi-<lb/>
<anchor type="note" xlink:label="note-0196-02a" xlink:href="note-0196-02"/>
am, et ſequentes praeſcribit delineationis leges. </s>
  <s xml:id="echoid-s3649" xml:space="preserve">1. </s>
  <s xml:id="echoid-s3650" xml:space="preserve">cryptarum, quae ue-<lb/>nas ab, cd, ef, ſequuntur, ueſtigium abdef pingit. </s>
  <s xml:id="echoid-s3651" xml:space="preserve">2. </s>
  <s xml:id="echoid-s3652" xml:space="preserve">addit loca puteorum <lb/>gh, ik, lm, qui ſuper uenarum meatibus erecti ſunt. </s>
  <s xml:id="echoid-s3653" xml:space="preserve">3. </s>
  <s xml:id="echoid-s3654" xml:space="preserve">deſcribit icbnograpbiam <lb/>menſionis ſubdialis, gopqrstu, 3. </s>
  <s xml:id="echoid-s3655" xml:space="preserve">quaerit lapſum et aſcenſus diſcrimen inter a <lb/>et m, idemque ſcala aſſumit, et lineam AB borizontalem ducit. </s>
  <s xml:id="echoid-s3656" xml:space="preserve">4. </s>
  <s xml:id="echoid-s3657" xml:space="preserve">Super bac bo-<lb/>rizontali erigit latera puteorum, ſecundum boram ipſis debitam, quando nempe <lb/>obliqui ſunt, ipſis uero lateribus gw, ix, ly tribuit altitudinem perpendicularens <lb/>bypotenuſae reſpondentem. </s>
  <s xml:id="echoid-s3658" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3659" xml:space="preserve">tandem per puteorum ſumma montis aream wxy <lb/>ducit. </s>
  <s xml:id="echoid-s3660" xml:space="preserve">Idem auctor recte monet, non melius intelligi ſcenographias, quam ſi cor-<lb/>pori v. </s>
  <s xml:id="echoid-s3661" xml:space="preserve">g. </s>
  <s xml:id="echoid-s3662" xml:space="preserve">argillae uel ligno ſcalae adminiculo inſcribantur primum altiſſimi tum <lb/>etiam ceteri putei deinde per ſuperiora eorum extrema menſio ſupra terram, per <lb/>inferiora menſio ſubterranea continuentur; </s>
  <s xml:id="echoid-s3663" xml:space="preserve">ſiquidem, facta corporis ſectione trans-<lb/>uerſa, ſecundum cuiuslibet directionis boram quaelibet crypta, uenaque, ſecundum <lb/>ſitum rectum uel obliquum inſculpi, atque ita ſodinarum quarumuis poſitio ad ui-<lb/>uum ueluti repraeſentari poteſt.</s>
  <s xml:id="echoid-s3664" xml:space="preserve"/>
</p>
<div xml:id="echoid-div177" type="float" level="2" n="1">
<note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">Figur. 25.</note>
</div>
</div>
<div xml:id="echoid-div179" type="section" level="1" n="133">
<head xml:id="echoid-head152" xml:space="preserve">SCHOLION II.</head>
<p style="it">
  <s xml:id="echoid-s3665" xml:space="preserve">107. </s>
  <s xml:id="echoid-s3666" xml:space="preserve">Atque baec ſunt, quae de geometria ſubterranea, lege metbodi matbe-<lb/>maticae tractata, eruditorum iudicio exponere nunc uiſum eſt. </s>
  <s xml:id="echoid-s3667" xml:space="preserve">Si <lb/>qua inpoſterum notatu non indigna, aut ad amplius illuſtrandum boc argumen-<lb/>tum ſpectantia occurrent, forfan plura et pleniora <lb/>ſequentur.</s>
  <s xml:id="echoid-s3668" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div180" type="section" level="1" n="134">
<head xml:id="echoid-head153" xml:space="preserve">S. D. G.</head>
<p>
  <s xml:id="echoid-s3669" xml:space="preserve">Corrigenda p. </s>
  <s xml:id="echoid-s3670" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3671" xml:space="preserve">§ 3. </s>
  <s xml:id="echoid-s3672" xml:space="preserve">lin. </s>
  <s xml:id="echoid-s3673" xml:space="preserve">5. </s>
  <s xml:id="echoid-s3674" xml:space="preserve">lege abduci p. </s>
  <s xml:id="echoid-s3675" xml:space="preserve">13. </s>
  <s xml:id="echoid-s3676" xml:space="preserve">§. </s>
  <s xml:id="echoid-s3677" xml:space="preserve">27. </s>
  <s xml:id="echoid-s3678" xml:space="preserve">lin. </s>
  <s xml:id="echoid-s3679" xml:space="preserve">6. </s>
  <s xml:id="echoid-s3680" xml:space="preserve">lege inquit enim</s>
</p>
<pb file="0197" n="202"/>
<pb file="0198" n="203"/>
  <figure>
    <image file="0198-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0198-01"/>
  </figure>
<pb file="0199" n="204"/>
  <figure>
    <image file="0199-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0199-01"/>
  </figure>
<pb file="0200" n="205"/>
<pb file="0201" n="206"/>
  <figure>
    <image file="0201-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0201-01"/>
  </figure>
<pb file="0202" n="207"/>
<pb file="0203" n="208"/>
<pb file="0204" n="209"/>
  <figure>
    <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0204-01"/>
  </figure>
<pb file="0205" n="210"/>
<pb file="0206" n="211"/>
<pb file="0207" n="212"/>
<pb file="0208" n="213"/>
  </div></text>
</echo>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Wed, 29 Nov 2017 16:55:37 +0100
parents	22d6a63640c6
children